Question

<1 and <2 are linear pair and <2 and 3 are vertical angles. M< 1 = (5y - 8) degrees and m<2 = (12 + 6y) degrees

What is m<3

16 degrees

72 degrees

108 degrees

132 degrees

Answer 1

m∠3 = 108°.

Since ∠1 and ∠2 are a linear pair, their sum is 180°. This means that
(5y-8)+(12+6y) = 180

Combine like terms:
11y+4 = 180

Subtract 4 from both sides:
11y+4-4=180-4
11y=176

Divide both sides by 11:
11y/11 = 176/11
y=16

We know that ∠3 and ∠2 are vertical angles; this means they are congruent. Substitute 16 for y in ∠2:
12+6y
12+6(16) = 12+96 = 108°