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SAT II Math I : Finding Angles

Study concepts, example questions & explanations for SAT II Math I

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Example Questions

Example Question #1 : Finding Angles

What angle do the minute and hour hands of a clock form at 4:45?

Possible Answers:

$137 \frac{1}{2}^{\circ }$

$117 \frac{1}{2}^{\circ }$

$127 \frac{1}{2}^{\circ }$

$122\frac{1}{2}^{\circ }$

$132\frac{1}{2}^{\circ }$

Correct answer:

$127 \frac{1}{2}^{\circ }$

Explanation:

There are twelve numbers on a clock; from one to the next, a hand rotates $\left (\frac{360}{12} \right )^{\circ } = 30^{\circ }$ . At 4:45, the minute hand is exactly on the "9" - that is, at the $\left (30 \times 9 \right )^{\circ }= 270^{\circ }$ . The hour hand is three-fourths of the way from the "4" to the "5" - that is, on the $\left (4 \frac{3}{4} \times 30 \right )^{\circ } = 142 \frac{1}{2} ^{\circ }$ position. Therefore, the difference is the angle they make:

$\left (270 - 142 \frac{1}{2} \right ) ^{\circ } = 127 \frac{1}{2}^{\circ }$

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Example Question #2 : Finding Angles

What angle do the minute and hour hands of a clock form at 8:50?

Possible Answers:

$55^{\circ }$

$35^ {\circ }$

$60^{\circ }$

$30^{\circ }$

$45^{\circ }$

Correct answer:

$35^ {\circ }$

Explanation:

There are twelve numbers on a clock; from one to the next, a hand rotates $\left (\frac{360}{12} \right )^{\circ } = 30^{\circ }$ . At 8:50, the minute hand is exactly on the "10" - that is, on the $\left (30 \times 10 \right )^{\circ }= 300^{\circ }$ position. The hour hand is five-sixth of the way from the "8" to the "9" - that is, on the $\left (8 \frac{5}{6} \times 30 \right )^{\circ } = 265 ^{\circ }$ position. Therefore, the difference is the angle they make:

$300^{\circ } - 265^{\circ } = 35^{\circ }$ .

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Example Question #3 : Finding Angles

Hexagon

Note: Figure NOT drawn to scale.

The above hexagon is regular. What is ?

Possible Answers:

x =72

x = 78

x = 51

x = 66

x = 84

Correct answer:

x = 66

Explanation:

Two of the angles of the quadrilateral formed are angles of a regular hexagon, so each measures

$\frac{180^{\circ } (6-2)}{6}= 120^{\circ }$ .

The four angles of the quadrilateral are $120 ^{\circ }, 120^{\circ } , x^{\circ }, (x - 12)^{\circ }$ . Their sum is $360^{\circ }$ , so we can set up, and solve for in, the equation:

x +(x-12)+ 120 + 120 =360

2x-12+ 120 + 120 =360

2x+228 =360

2x =132

x = 66

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Example Question #1 : Finding Angles

Can a triangle have a set of angles that are 90, 46, and degrees?

Possible Answers:

Yes

Correct answer:

Explanation:

A triangle's angles must add up to 180 degrees.

The angles given add up to 181,

(90+46+45=181) .

That means that this cannot be an actual triangle.

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Example Question #5 : Finding Angles

If two angles of a triangle are $60^{\circ}$ and $75.5^{\circ}$ , find the measurement of the third angle.

Possible Answers:

$44.5^{\circ}$

$45^{\circ}$

$180^{\circ}$

Correct answer:

$44.5^{\circ}$

Explanation:

Step 1: Recall the sum of the angles of a triangle...

The sum of the internal angles of a triangle is $180^{\circ}$ .

Step 2: To find the missing angle, subtract the given angles from $180^{\circ}$ ...

$180^{\circ}-60^{\circ}-75.5^{\circ}=44.5^{\circ}$

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SAT II Math I : Finding Angles

Study concepts, example questions & explanations for SAT II Math I

All SAT II Math I Resources

Example Questions

Example Question #1 : Finding Angles

Example Question #2 : Finding Angles

Example Question #3 : Finding Angles

Example Question #1 : Finding Angles

Example Question #5 : Finding Angles

All SAT II Math I Resources

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