Chapter 2.2, Problem 17PSB

To determine

To Prove: $\angle ABF$ and $\angle EBD$ are complementary.

Explanation of Solution

Given information:

  

Formula Used: linear pair axiom ; sum of complementary angle is ${90}^{\circ }$

Proof:

  $\because$ ABC is a line, then by linear pair axiom,

  $\begin{array}{l}\angle ABF+\angle FBE+\angle EBD+\angle DBC={180}^{\circ },\\ \therefore x^{\circ }+x^{\circ }+y^{\circ }+y^{\circ }={180}^{\circ }\\ \therefore 2(x^{\circ }+y^{\circ })={180}^{\circ }\\ \therefore x^{\circ }+y^{\circ }={90}^{\circ }\\ \therefore \angle ABF+\angle EBD={90}^{\circ }\end{array}$

Hence $\angle ABF$ and $\angle EBD$ are complementary.