Question

In the figure, angle D measures 127° and angle A measures 75°.

Answer 1

C=180-D

C=53

B=180-(53+75)

B=180-128

B=52 degrees

Answer 2

Answer:

The measure of angle B is 52 degrees.

Step-by-step explanation:

Given information: ∠D=127°, ∠A=75°.

The measurement of angle B.

b = 180° – 75° – (°? – 127°)

According to the angle sum property, the sum of interior angles of a triangle is 180 degrees.

$\angle A+\angle B+\angle C=180^{\circ}$

$75^{\circ}+\angle B+\angle C=180^{\circ}$           .... (1)

Angle D is exterior angle of angle C. So, angle C and D are supplementary angles and their sum is 180 degrees.

$\angle C+\angle D=180^{\circ}$

$\angle C+127^{\circ}=180^{\circ}$

$\angle C=180^{\circ}-127^{\circ}$                         .... (2)

From (1) and (2)  we get

$75^{\circ}+\angle B+(180^{\circ}-127^{\circ})=180^{\circ}$

$\angle B=180^{\circ}-75^{\circ}-(180^{\circ}-127^{\circ})$

Therefore the missing value in the given equation is 180.

$\angle B=180^{\circ}-75^{\circ}-180^{\circ}+127^{\circ}$

$\angle B=52^{\circ}$

Therefore the measure of angle B is 52 degrees.