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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}$$

$147.5$^{\circ}$$

$75$^{\circ}$$

$300.5$^{\circ}$$

$300$^{\circ}$$

Correct answer:

$295$^{\circ}$$

Explanation:

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

180 (n-2) degrees, where 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: 180(4-2) degrees =180(2) degrees =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 degrees and the sum of the non-congruent opposite angles.

The solution is:

40+25=65

360-65=295 degrees

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

Check:

295+65=360

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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 $28$^{\circ}$$ and $84$^{\circ}$$ , respectively. Find the measurement for one of the two remaining interior angles in this kite.

Possible Answers:

$124$^{\circ}$$

Not enough information is provided

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

$248$^{\circ}$$

$112$^{\circ}$$

Correct answer:

$124$^{\circ}$$

Explanation:

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

180 (n-2) degrees, where 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: 180(4-2) degrees =180(2) degrees =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 degrees and the non-congruent opposite angles sum by :

28+84=112

360-112=248

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

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

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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}$$ and $51$^{\circ}$$ , respectively. Find the measurement for one of the two remaining interior angles in this kite.

Possible Answers:

$95$^{\circ}$$

$95.5$^{\circ}$$

$191$^{\circ}$$

$169$^{\circ}$$

$59.5$^{\circ}$$

Correct answer:

$95.5$^{\circ}$$

Explanation:

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

180 (n-2) degrees, where 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: 180(4-2) degrees =180(2) degrees =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 degrees and the non-congruent opposite angles sum by :

118+51=169

360-169=191

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

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

Report an Error

Example Question #1 : Quadrilaterals

Kite vt act

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

Possible Answers:

$132.5$^{\circ}$$

$285$^{\circ}$$

$265$^{\circ}$$

$85$^{\circ}$$

$275$^{\circ}$$

Correct answer:

$285$^{\circ}$$

Explanation:

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

180 (n-2) degrees, where 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: 180(4-2) degrees =180(2) degrees =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 degrees and the sum of the non-congruent opposite angles.

The solution is:

45+30=75

360-75=285 degrees

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

Report an Error

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}$$ and $99$^{\circ}$$ , respectively. Find the measurement for one of the two remaining interior angles in this kite.

Possible Answers:

$95$^{\circ}$$

$72$^{\circ}$$

$85$^{\circ}$$

$170$^{\circ}$$

$190$^{\circ}$$

Correct answer:

$85$^{\circ}$$

Explanation:

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

180 (n-2) degrees, where 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: 180(4-2) degrees =180(2) degrees =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 degrees and the non-congruent opposite angles sum by :

91+99=190

360-190=170

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

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

Report an Error

Example Question #2 : Quadrilaterals

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

Possible Answers:

$140$^{\circ}$$

$240$^{\circ}$$

$105$^{\circ}$$

$220$^{\circ}$$

$110$^{\circ}$$

Correct answer:

$220$^{\circ}$$

Explanation:

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

180 (n-2) degrees, where 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: 180(4-2) degrees =180(2) degrees =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 degrees and the sum of the non-congruent opposite angles.

The solution is:

82+58=140

360-140=220 degrees

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

Check:

110+110+58+82=360

Report an Error

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 $204$^{\circ}$$ and $36$^{\circ}$$ , respectively. Find the measurement for one of the two remaining interior angles in this kite.

Possible Answers:

$140$^{\circ}$$

$60$^{\circ}$$

$240$^{\circ}$$

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

$120$^{\circ}$$

Correct answer:

$60$^{\circ}$$

Explanation:

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

180 (n-2) degrees, where 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: 180(4-2) degrees =180(2) degrees =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 degrees and the non-congruent opposite angles sum by :

204+36=240

360-240=120

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

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

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 $112$^{\circ}$$ and $101$^{\circ}$$ , respectively. Find the measurement of the sum of the two remaining interior angles.

Possible Answers:

$147$^{\circ}$$

$213$^{\circ}$$

$67.5$^{\circ}$$

$62$^{\circ}$$

$101$^{\circ}$$

Correct answer:

$147$^{\circ}$$

Explanation:

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

180 (n-2) degrees, where 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: 180(4-2) degrees =180(2) degrees =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 degrees and the sum of the non-congruent opposite angles.

The solution is:

112+101=213

360-213=147 degrees

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

Check:

213+147=360

Report an Error

Example Question #6 : How To Find An Angle In A Kite

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

Possible Answers:

$87.5$^{\circ}$$

$78.5$^{\circ}$$

$203$^{\circ}$$

$157$^{\circ}$$

$204.5$^{\circ}$$

Correct answer:

$78.5$^{\circ}$$

Explanation:

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

180 (n-2) degrees, where 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: 180(4-2) degrees =180(2) degrees =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 degrees and the non-congruent opposite angles sum by :

16+187=203

360-203=157

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

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

Report an Error

Example Question #3 : Quadrilaterals

Kite vt act

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

Possible Answers:

$187.5$^{\circ}$$

$264$^{\circ}$$

$106$^{\circ}$$

$87.5$^{\circ}$$

$175$^{\circ}$$

Correct answer:

$175$^{\circ}$$

Explanation:

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

180 (n-2) degrees, where 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: 180(4-2) degrees =180(2) degrees =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 degrees and the sum of the non-congruent opposite angles.

The solution is:

53+132=185 degrees

360-185=175 degrees

Thus, 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 #2 : How To Find An Angle In A Kite

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

Example Question #1 : Quadrilaterals

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

Example Question #2 : Quadrilaterals

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

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

Example Question #6 : How To Find An Angle In A Kite

Example Question #3 : Quadrilaterals

All ACT Math Resources

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