Question

∠1 and ∠2 are supplementary angles. If m∠1 = (7x + 18)∘ and m∠2 = (x + 18)∘, then find the measure of ∠1.

Answer 1

Since ∠1 and ∠2 are supplementary angles, we know that their measures add up to 180°.

So, we can write the equation:

m∠1 + m∠2 = 180°
(7x + 18) + (x + 18) = 180
8x + 36 = 180
8x = 144
x = 18

Now that we have found the value of x, we can substitute it back into the measure of ∠1:

m∠1 = (7x + 18)∘
m∠1 = 7(18) + 18
m∠1 = 126 + 18
m∠1 = 144°

Therefore, the measure of ∠1 is 144°.