Geometry angles relationships & Algebra

Question

∠1, ∠2, and ∠3 are adjacent angles, with ∠1 supplementary to ∠2 and ∠2 complementary

to ∠3. If m∠1 = (8x + 3)° and m∠2 = (5x – 18)°, find m∠3.

Answer 1

Supplementary means that the angles associated add up to 180 degrees

Complementary means that the angles associated add up to 90 degrees

so that means m∠1 + m∠2 = 180°

8x+3 + 5x-18 = 180

13x-15=180

x=15

plugging in x to our angle measures you'll find that m∠1=123° and the m∠2=57° which indeed adds up to 180°

now ∠2 and ∠3 are complementary so m∠2 + m∠3 =90°

we can plug in for m∠2 which we found to be 57°, so we get ∋

57 + m∠3 = 90 therefore m∠3 = 33°