∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left bracket, x, plus, 15, right bracket, degrees∠1=(x+15)
∘
and mangle, 2, equals, left bracket, 5, x, minus, 17, right bracket, degrees∠2=(5x−17)
∘
, then find the measure of angle, 2∠2.
Since ∠1 and ∠2 are vertical angles, they are equal in measure. Therefore, we have:
∠1 = ∠2
x + 15 = 5x - 17
Solving this equation for x, we get:
4x = 32
x = 8
Now we can find the measure of ∠2:
∠2 = 5x - 17
∠2 = 5(8) - 17
∠2 = 40 - 17
∠2 = 23 degrees
Therefore, the measure of ∠2 is 23 degrees.