Question

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

Answer 1

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°