Question

The sum of the measures of the angles in △ABC is 180°. The sum of the measures of angle B and angle C is twice the measure of angle A. The measure of angle B is 32° less than the measure of angle C.

Answer 1

< A = 60 degrees.

< B = 44 degrees

<C = 76 degrees.

Explanation:

A + B + C = 180 --------(1)

2A = B + C -------(2)

B = C - 32 -------(3)

We see from equation 2 that B + C = 2A so we

replace The A + B in equation (1) by 2A:

A + 2A = 180

3A = 180

A = 60.

Substitute A = 60 in equation (2):

120 = B + C

Rearranging equation (3):

32 = -B + C

Adding theses last 2 equations:

152 = 2C

C = 152/2 = 76.

Substituting for A and C in equation (1):

60 + 76 + B = 180

B = 180 - 60 - 76 = 44 degrees.