If the measure of an angle is twice the measure of its complement, find the angle.

Step-by-step explanation:

Suppose two angles ∠A and ∠B of measures x and y

A and B are complementary means x + y = 90

the measure of ∠B is twice the measure of ∠A means y = 2x

then we have to solve the system

x + y = 90

y = 2x

then

x + 2x = 90

then

3x = 90

then x = 90/3

         = 30

therefore

y = 2×(30)

 = 60

:)

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60⁰

Step-by-step explanation:

Angle = x

Complement = 90 - x

Given:

x = 2 (90 - x)

x = 180 - 2x

3x = 180

x = 60⁰

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

.95

step-by-step explanation: