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tatyana61 [14]
3 years ago
12

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

Mathematics
2 answers:
Slav-nsk [51]3 years ago
6 0
C=180-D

C=53

B=180-(53+75)

B=180-128

B=52 degrees
spayn [35]3 years ago
5 0

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.

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Step-by-step explanation:

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