∠A and ∠ B ∠B are supplementary angles. If m ∠ A = ( 2 x + 27 ) ∘ ∠A=(2x+27) ∘ and m ∠ B = ( x + 27 ) ∘ ∠B=(x+27) ∘ , then find the measure of ∠ B ∠B

Question

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Respuesta :

MrRoyal MrRoyal · Answer 1 · 2020-12-12T01:06:21+01:00

Answer:

[tex]B = 69[/tex]

Step-by-step explanation:

Given

[tex]A = 2x +27[/tex]

[tex]B = x +27[/tex]

Required

Determine B

First, we need to solve for x

Since both angles are supplementary, then

[tex]A + B = 180[/tex]

Substitute values for A and B

[tex]2x + 27 + x + 27 = 180[/tex]

Collect Like Terms

[tex]2x + x = 180 - 27 - 27[/tex]

[tex]3x= 126[/tex]

Divide through by 3

[tex]x = 42[/tex]

Recall that:

[tex]B = x +27[/tex]

Substitute 42 for x

[tex]B = 42 + 27[/tex]

[tex]B = 69[/tex]