The measure of angle A is 45^\circ greater than the measure of angle B. If the measure of … — SAT

The measure of angle $A$ is $45^\circ$ greater than the measure of angle $B$ . If the measure of angle $B$ is $\frac{5\pi}{12}$ radians, what is the measure of angle $A$ , in degrees?

Answer: 120

Answer

120

The correct answer is 120. First, convert the measure of angle

B

from radians to degrees:

\frac{5\pi}{12} \times \frac{180}{\pi} = \frac{5 \times 180}{12} = 5 \times 15 = 75^\circ

. Since angle

A

45^\circ

greater than angle

B

, add

45^\circ

to the measure of angle

B

75^\circ + 45^\circ = 120^\circ

Step-by-Step Solution

Convert the measure of angle

B

from radians to degrees.

Angle

B

has a measure of

75^\circ

To convert from radians to degrees, multiply the radian measure by

\frac{180}{\pi}

Calculate the measure of angle

A

by adding

45^\circ

to the measure of angle

B

Angle

A

has a measure of

120^\circ

It is given that the measure of angle

A

45^\circ

greater than the measure of angle

B

Key Concept

To convert an angle from radians to degrees, multiply the angle measure in radians by

\frac{180}{\pi}

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