angles for geom

Question

∠1 and angle, 2∠2 are supplementary angles. If m, angle, 1, equals, left parenthesis, 7, x, plus, 18, right parenthesis, degreesm∠1=(7x+18)∘ and m, angle, 2, equals, left parenthesis, x, plus, 18, right parenthesis, degreesm∠2=(x+18)∘, then find the measure of angle, 1∠1.

Answer 1

If ∠1 and ∠2 are supplementary angles, then m∠1 + m∠2 = 180°. We can set up an algebraic equation for this:

(7x + 18) + (x + 18) = 180

8x + 36 = 180

8x = 144

x = 18

Remember, m∠1 = 7x + 18, so we substitute the x we found into our equation:

m∠1 = 7(18) + 18 = 144°

Hope this was helpful.