182k views
1 vote
1. Lines p and q are intersected by line r, such that line p is parallel to line q. If m<1=7x - 36 and m<2 = 5x+12, what is the m<1

1. Lines p and q are intersected by line r, such that line p is parallel to line q-example-1

1 Answer

4 votes

We are given a figure in which line r intersects two parallel lines p and q.

The angles labeled as ∠1 and ∠2 are known as same-side interior angles.

Same-side interior angles are supplementary meaning that their sum is equal to 180°.

So we can write,


\begin{gathered} \angle1+\angle2=180\degree \\ (7x-36)+(5x+12)=180\degree \end{gathered}

Now let us solve this equation for x.


\begin{gathered} 7x+5x-36+12=180 \\ 12x-24=180 \\ 12x=180+24 \\ 12x=204 \\ x=(204)/(12) \\ x=17\degree \end{gathered}

Now we can find the exact value of the angle ∠1


\angle1=7x-36=7(17)-36=119-36=83\degree

Therefore, angle ∠1 = 83°

User Geo Ego
by
7.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories