Question

Prove that sum of all interior angles in the shown triangle is equal to ${180}^{\circ }$

Answer 1

For lines $XY$ and $QR$ with transversal $PQ$

$\angle 2=\angle 4$(alternate angles) ....$\left(1\right)$

For lines $XY$ and $QR$ with transversal $PR$

$\angle 3=\angle 5$(alternate angles) ....$\left(2\right)$

Also, for line $XY$

$\angle 1+\angle 4+\angle 5={180}^{\circ }$(Linear pair)

$\angle 1+\angle 2+\angle 3={180}^{\circ }$ from $\left(1\right)$ and $\left(2\right)$

Hence proved.