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ACT Math : Quadrilaterals

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Example Questions

Example Question #1 : How To Find An Angle In A Kite

Kite vt act

Using the kite shown above, find the sum of the two remaining congruent interior angles.

Possible Answers:

$295$^{\circ}$$ $\displaystyle 295$^{\circ}$$

$300$^{\circ}$$ $\displaystyle 300$^{\circ}$$

$75$^{\circ}$$ $\displaystyle 75$^{\circ}$$

$300.5$^{\circ}$$ $\displaystyle 300.5$^{\circ}$$

$147.5$^{\circ}$$ $\displaystyle 147.5$^{\circ}$$

Correct answer:

$295$^{\circ}$$ $\displaystyle 295$^{\circ}$$

Explanation:

The sum of the interior angles of any polygon can be found by applying the formula:

$\displaystyle 180 (n-2)$ degrees, where $\displaystyle n$ is the number of sides in the polygon.

By definition, a kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: $\displaystyle 180(4-2)$ degrees =180(2) $\displaystyle =180(2)$ degrees =360 $\displaystyle =360$ degrees. Additionally, kites must have two sets of equivalent adjacent sides & one set of congruent opposite angles.

To find the sum of the remaining two angles, determine the difference between 360 $\displaystyle 360$ degrees and the sum of the non-congruent opposite angles.

The solution is:

$\displaystyle 40+25=65$

$\displaystyle 360-65=295$ degrees

Thus, 295 $\displaystyle 295$ degrees is the sum of the remaining two opposite angles.

Check:

$\displaystyle 295+65=360$

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Example Question #1 : How To Find An Angle In A Kite

A kite has one set of opposite interior angles where the two angles measure $28$^{\circ}$$ $\displaystyle 28$^{\circ}$$ and $84$^{\circ}$$ $\displaystyle 84$^{\circ}$$, respectively. Find the measurement for one of the two remaining interior angles in this kite.

Possible Answers:

$112$^{\circ}$$ $\displaystyle 112$^{\circ}$$

$248$^{\circ}$$ $\displaystyle 248$^{\circ}$$

$124$^{\circ}$$ $\displaystyle 124$^{\circ}$$

$84^2$^{\circ}$$ $\displaystyle 84^2$^{\circ}$$

Not enough information is provided

Correct answer:

$124$^{\circ}$$ $\displaystyle 124$^{\circ}$$

Explanation:

The sum of the interior angles of any polygon can be found by applying the formula:

$\displaystyle 180 (n-2)$ degrees, where $\displaystyle n$ is the number of sides in the polygon.

By definition, a kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: $\displaystyle 180(4-2)$ degrees =180(2) $\displaystyle =180(2)$ degrees =360 $\displaystyle =360$ degrees. Additionally, kites must have two sets of equivalent adjacent sides & one set of congruent opposite angles.

The missing angle can be found by finding the sum of the non-congruent opposite angles. Then divide the difference between 360 $\displaystyle 360$ degrees and the non-congruent opposite angles sum by $\displaystyle 2$:

$\displaystyle 28+84=112$

$\displaystyle 360-112=248$

This means that 248 $\displaystyle 248$ is the sum of the remaining two angles, which must be opposite congruent angles. Therefore, the measurement for one of the angles is:

$\frac{248}{2}=124$ $\displaystyle \frac{248}{2}=124$

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Example Question #1 : How To Find An Angle In A Kite

A kite has one set of opposite interior angles where the two angles measure $118$^{\circ}$$ $\displaystyle 118$^{\circ}$$ and $51$^{\circ}$$ $\displaystyle 51$^{\circ}$$, respectively. Find the measurement for one of the two remaining interior angles in this kite.

Possible Answers:

$59.5$^{\circ}$$ $\displaystyle 59.5$^{\circ}$$

$95.5$^{\circ}$$ $\displaystyle 95.5$^{\circ}$$

$169$^{\circ}$$ $\displaystyle 169$^{\circ}$$

$95$^{\circ}$$ $\displaystyle 95$^{\circ}$$

$191$^{\circ}$$ $\displaystyle 191$^{\circ}$$

Correct answer:

$95.5$^{\circ}$$ $\displaystyle 95.5$^{\circ}$$

Explanation:

The sum of the interior angles of any polygon can be found by applying the formula:

$\displaystyle 180 (n-2)$ degrees, where $\displaystyle n$ is the number of sides in the polygon.

A kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: $\displaystyle 180(4-2)$ degrees =180(2) $\displaystyle =180(2)$ degrees =360 $\displaystyle =360$ degrees. Additionally, kites must have two sets of equivalent adjacent sides & one set of congruent opposite angles.

The missing angle can be found by finding the sum of the non-congruent opposite angles. Then divide the difference between 360 $\displaystyle 360$ degrees and the non-congruent opposite angles sum by $\displaystyle 2$:

$\displaystyle 118+51=169$

$\displaystyle 360-169=191$

This means that 191 $\displaystyle 191$ is the sum of the remaining two angles, which must be opposite congruent angles. Therefore, the measurement for one of the angles is:

$\frac{191}{2}=95.5$ $\displaystyle \frac{191}{2}=95.5$

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Example Question #2 : How To Find An Angle In A Kite

Kite vt act

Using the kite shown above, find the sum of the two remaining congruent interior angles.

Possible Answers:

$275$^{\circ}$$ $\displaystyle 275$^{\circ}$$

$85$^{\circ}$$ $\displaystyle 85$^{\circ}$$

$285$^{\circ}$$ $\displaystyle 285$^{\circ}$$

$265$^{\circ}$$ $\displaystyle 265$^{\circ}$$

$132.5$^{\circ}$$ $\displaystyle 132.5$^{\circ}$$

Correct answer:

$285$^{\circ}$$ $\displaystyle 285$^{\circ}$$

Explanation:

The sum of the interior angles of any polygon can be found by applying the formula:

$\displaystyle 180 (n-2)$ degrees, where $\displaystyle n$ is the number of sides in the polygon.

A kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: $\displaystyle 180(4-2)$ degrees =180(2) $\displaystyle =180(2)$ degrees =360 $\displaystyle =360$ degrees. Additionally, kites must have two sets of equivalent adjacent sides & one set of congruent opposite angles.

To find the sum of the remaining two angles, determine the difference between 360 $\displaystyle 360$ degrees and the sum of the non-congruent opposite angles.

The solution is:

$\displaystyle 45+30=75$

$\displaystyle 360-75=285$ degrees

Thus, 285 $\displaystyle 285$ degrees is the sum of the remaining two opposite angles.

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Example Question #3 : How To Find An Angle In A Kite

A kite has one set of opposite interior angles where the two angles measure $91$^{\circ}$$ $\displaystyle 91$^{\circ}$$ and $99$^{\circ}$$ $\displaystyle 99$^{\circ}$$ , respectively. Find the measurement for one of the two remaining interior angles in this kite.

Possible Answers:

$170$^{\circ}$$ $\displaystyle 170$^{\circ}$$

$72$^{\circ}$$ $\displaystyle 72$^{\circ}$$

$95$^{\circ}$$ $\displaystyle 95$^{\circ}$$

$85$^{\circ}$$ $\displaystyle 85$^{\circ}$$

$190$^{\circ}$$ $\displaystyle 190$^{\circ}$$

Correct answer:

$85$^{\circ}$$ $\displaystyle 85$^{\circ}$$

Explanation:

The sum of the interior angles of any polygon can be found by applying the formula:

$\displaystyle 180 (n-2)$ degrees, where $\displaystyle n$ is the number of sides in the polygon.

By definition, a kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: $\displaystyle 180(4-2)$ degrees =180(2) $\displaystyle =180(2)$ degrees =360 $\displaystyle =360$ degrees. Additionally, kites must have two sets of equivalent adjacent sides & one set of congruent opposite angles.

The missing angle can be found by finding the sum of the non-congruent opposite angles. Then divide the difference between 360 $\displaystyle 360$ degrees and the non-congruent opposite angles sum by $\displaystyle 2$:

$\displaystyle 91+99=190$

$\displaystyle 360-190=170$

This means that 170 $\displaystyle 170$ is the sum of the remaining two angles, which must be opposite congruent angles. Therefore, the measurement for one of the angles is:

$\frac{170}{2}=85$ $\displaystyle \frac{170}{2}=85$

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Example Question #4 : How To Find An Angle In A Kite

A kite has one set of opposite interior angles where the two angles measure $82$^{\circ}$$ $\displaystyle 82$^{\circ}$$ and $58$^{\circ}$$ $\displaystyle 58$^{\circ}$$, respectively. Find the measurement of the sum of the two remaining interior angles in this kite.

Possible Answers:

$110$^{\circ}$$ $\displaystyle 110$^{\circ}$$

$240$^{\circ}$$ $\displaystyle 240$^{\circ}$$

$105$^{\circ}$$ $\displaystyle 105$^{\circ}$$

$140$^{\circ}$$ $\displaystyle 140$^{\circ}$$

$220$^{\circ}$$ $\displaystyle 220$^{\circ}$$

Correct answer:

$220$^{\circ}$$ $\displaystyle 220$^{\circ}$$

Explanation:

The sum of the interior angles of any polygon can be found by applying the formula:

$\displaystyle 180 (n-2)$ degrees, where $\displaystyle n$ is the number of sides in the polygon.

By definition, a kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: $\displaystyle 180(4-2)$ degrees =180(2) $\displaystyle =180(2)$ degrees =360 $\displaystyle =360$ degrees. Additionally, kites must have two sets of equivalent adjacent sides & one set of congruent opposite angles.

To find the sum of the remaining two angles, determine the difference between 360 $\displaystyle 360$ degrees and the sum of the non-congruent opposite angles.

The solution is:

$\displaystyle 82+58=140$

$\displaystyle 360-140=220$ degrees

This means that 220 $\displaystyle 220$ degrees is the sum of the remaining two opposite angles and that each have an individual measurement of 110 $\displaystyle 110$ degrees.

Check:

$\displaystyle 110+110+58+82=360$

Report an Error

Example Question #5 : How To Find An Angle In A Kite

A kite has one set of opposite interior angles where the two angles measure $204$^{\circ}$$ $\displaystyle 204$^{\circ}$$ and $36$^{\circ}$$ $\displaystyle 36$^{\circ}$$, respectively. Find the measurement for one of the two remaining interior angles in this kite.

Possible Answers:

$60$^{\circ}$$ $\displaystyle 60$^{\circ}$$

$120$^{\circ}$$ $\displaystyle 120$^{\circ}$$

$\sqrt{240}$^{\circ}$$ $\displaystyle \sqrt{240}$^{\circ}$$

$140$^{\circ}$$ $\displaystyle 140$^{\circ}$$

$240$^{\circ}$$ $\displaystyle 240$^{\circ}$$

Correct answer:

$60$^{\circ}$$ $\displaystyle 60$^{\circ}$$

Explanation:

The sum of the interior angles of any polygon can be found by applying the formula:

$\displaystyle 180 (n-2)$ degrees, where $\displaystyle n$ is the number of sides in the polygon.

A kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: $\displaystyle 180(4-2)$ degrees =180(2) $\displaystyle =180(2)$ degrees =360 $\displaystyle =360$ degrees. Additionally, kites must have two sets of equivalent adjacent sides & one set of congruent opposite angles.

The missing angle can be found by finding the sum of the non-congruent opposite angles. Then divide the difference between 360 $\displaystyle 360$ degrees and the non-congruent opposite angles sum by $\displaystyle 2$:

$\displaystyle 204+36=240$

$\displaystyle 360-240=120$

This means that 120 $\displaystyle 120$ is the sum of the remaining two angles, which must be opposite congruent angles. Therefore, the measurement for one of the angles is:

$\frac{120}{2}=60$ $\displaystyle \frac{120}{2}=60$

Report an Error

Example Question #2 : How To Find An Angle In A Kite

A kite has one set of opposite interior angles where the two angles measure $112$^{\circ}$$ $\displaystyle 112$^{\circ}$$ and $101$^{\circ}$$ $\displaystyle 101$^{\circ}$$, respectively. Find the measurement of the sum of the two remaining interior angles.

Possible Answers:

$213$^{\circ}$$ $\displaystyle 213$^{\circ}$$

$67.5$^{\circ}$$ $\displaystyle 67.5$^{\circ}$$

$147$^{\circ}$$ $\displaystyle 147$^{\circ}$$

$101$^{\circ}$$ $\displaystyle 101$^{\circ}$$

$62$^{\circ}$$ $\displaystyle 62$^{\circ}$$

Correct answer:

$147$^{\circ}$$ $\displaystyle 147$^{\circ}$$

Explanation:

The sum of the interior angles of any polygon can be found by applying the formula:

$\displaystyle 180 (n-2)$ degrees, where $\displaystyle n$ is the number of sides in the polygon.

By definition, a kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: $\displaystyle 180(4-2)$ degrees =180(2) $\displaystyle =180(2)$ degrees =360 $\displaystyle =360$ degrees. Additionally, kites must have two sets of equivalent adjacent sides & one set of congruent opposite angles.

To find the sum of the remaining two angles, determine the difference between 360 $\displaystyle 360$ degrees and the sum of the non-congruent opposite angles.

The solution is:

$\displaystyle 112+101=213$

$\displaystyle 360-213=147$ degrees

This means that 147 $\displaystyle 147$ degrees is the sum of the remaining two opposite angles.

Check:

$\displaystyle 213+147=360$

Report an Error

Example Question #2 : How To Find An Angle In A Kite

A kite has one set of opposite interior angles where the two angles measure $16$^{\circ}$$ $\displaystyle 16$^{\circ}$$ and $187$^{\circ}$$ $\displaystyle 187$^{\circ}$$, respectively. Find the measurement for one of the two remaining interior angles in this kite.

Possible Answers:

$78.5$^{\circ}$$ $\displaystyle 78.5$^{\circ}$$

$204.5$^{\circ}$$ $\displaystyle 204.5$^{\circ}$$

$87.5$^{\circ}$$ $\displaystyle 87.5$^{\circ}$$

$203$^{\circ}$$ $\displaystyle 203$^{\circ}$$

$157$^{\circ}$$ $\displaystyle 157$^{\circ}$$

Correct answer:

$78.5$^{\circ}$$ $\displaystyle 78.5$^{\circ}$$

Explanation:

The sum of the interior angles of any polygon can be found by applying the formula:

$\displaystyle 180 (n-2)$ degrees, where $\displaystyle n$ is the number of sides in the polygon.

By definition, a kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: $\displaystyle 180(4-2)$ degrees =180(2) $\displaystyle =180(2)$ degrees =360 $\displaystyle =360$ degrees. Additionally, kites must have two sets of equivalent adjacent sides & one set of congruent opposite angles.

The missing angle can be found by finding the sum of the non-congruent opposite angles. Then divide the difference between 360 $\displaystyle 360$ degrees and the non-congruent opposite angles sum by $\displaystyle 2$:

$\displaystyle 16+187=203$

$\displaystyle 360-203=157$

This means that 157 $\displaystyle 157$ is the sum of the remaining two angles, which must be opposite congruent angles. Therefore, the measurement for one of the angles is:

$\frac{157}{2}=78.5$ $\displaystyle \frac{157}{2}=78.5$

Report an Error

Example Question #1 : How To Find An Angle In A Kite

Kite vt act

Using the kite shown above, find the sum of the two remaining congruent interior angles.

Possible Answers:

$187.5$^{\circ}$$ $\displaystyle 187.5$^{\circ}$$

$175$^{\circ}$$ $\displaystyle 175$^{\circ}$$

$264$^{\circ}$$ $\displaystyle 264$^{\circ}$$

$87.5$^{\circ}$$ $\displaystyle 87.5$^{\circ}$$

$106$^{\circ}$$ $\displaystyle 106$^{\circ}$$

Correct answer:

$175$^{\circ}$$ $\displaystyle 175$^{\circ}$$

Explanation:

The sum of the interior angles of any polygon can be found by applying the formula:

$\displaystyle 180 (n-2)$ degrees, where $\displaystyle n$ is the number of sides in the polygon.

A kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: $\displaystyle 180(4-2)$ degrees =180(2) $\displaystyle =180(2)$ degrees =360 $\displaystyle =360$ degrees. Additionally, kites must have two sets of equivalent adjacent sides & one set of congruent opposite angles.

To find the sum of the remaining two angles, determine the difference between 360 $\displaystyle 360$ degrees and the sum of the non-congruent opposite angles.

The solution is:

$\displaystyle 53+132=185$ degrees

$\displaystyle 360-185=175$ degrees

Thus, 175 $\displaystyle 175$ degrees is the sum of the remaining two opposite angles.

Report an Error

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ACT Math : Quadrilaterals

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Find An Angle In A Kite

Example Question #1 : How To Find An Angle In A Kite

Example Question #1 : How To Find An Angle In A Kite

Example Question #2 : How To Find An Angle In A Kite

Example Question #3 : How To Find An Angle In A Kite

Example Question #4 : How To Find An Angle In A Kite

Example Question #5 : How To Find An Angle In A Kite

Example Question #2 : How To Find An Angle In A Kite

Example Question #2 : How To Find An Angle In A Kite

Example Question #1 : How To Find An Angle In A Kite

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