Chapter 5.3, Problem 19PSB

To determine

To Prove: $\angle A+\angle B={180}^{\circ }$ .

Explanation of Solution

Given:

  

  $\angle C+\angle D={180}^{\circ }$

Concept Used:

When two parallel lines are intersected by a transversal angles on the same side of transversal are supplementary.

Sum of angles of a quadrilateral is ${360}^{\circ }$

Proof:

Here, we have

  $\angle C+\angle D={180}^{\circ }$

Since sum of angles of a quadrilateral is ${360}^{\circ }$

  $\begin{array}{l}\angle A+\angle B+\angle C+\angle D={360}^{\circ }\\ \Rightarrow \angle A+\angle B+{180}^{\circ }={360}^{\circ }\\ \Rightarrow \angle A+\angle B={180}^{\circ }\end{array}$