math is hard and i need help

Question

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

Answer 1

Hi Bailey,

Since ∠1 and ∠2 are supplementary, it follows by definition that their sum is 180°. That is,

m∠1+m∠2=180º. Furthermore, given that m∠1=7x+18 and m∠2=x+18, by substitution we write:

(7x+18)+(x+18)=180. Hence, (7x+x)+(18+18)=180 by the associative and commutative properties of addition. So that if we simplify (add like term), we have 8x+36=180. Solving this equation for x, we inverse operate by first subtracting 36 on both side and then divide the resulting equation by 8, as follows:

8x+36-36=180-36 ⇒ 8x=144 ⇒ 8x/8 = 144/8 ⇒ x=18

Substitute x=18 into m∠1=7x+18 ⇒ m∠1=7(18)+18 ⇒ m∠1=144°

As you learn the language of mathematics, what was once hard is extremely fun! Stay motivated Baily.

Hope this helps.