Question

∠1 and ∠2 are vertical angles. If m∠1 = (x + 12)∘ and m∠2 = (6x - 8)∘, then find the measure of ∠2.

Answer 1

Since ∠1 and ∠2 are vertical angles, they are congruent. Therefore, we can set up an equation:

m∠1 = m∠2
(x + 12) = (6x - 8)

Now, solve for x:

x + 12 = 6x - 8
20 = 5x
x = 4

Now, substitute x = 4 back into the equation for ∠2:

m∠2 = (6(4) - 8) = 24 - 8 = 16

Therefore, the measure of ∠2 is 16 degrees.