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,
[tex]\begin{gathered} \angle1+\angle2=180\degree \\ (7x-36)+(5x+12)=180\degree \end{gathered}[/tex]
Now let us solve this equation for x.
[tex]\begin{gathered} 7x+5x-36+12=180 \\ 12x-24=180 \\ 12x=180+24 \\ 12x=204 \\ x=\frac{204}{12} \\ x=17\degree \end{gathered}[/tex]
Now we can find the exact value of the angle ∠1
[tex]\angle1=7x-36=7(17)-36=119-36=83\degree[/tex]
Therefore, angle ∠1 = 83°
