Chapter 2.5, Problem 8PSA

To determine

To prove: $\angle T=\angle X$

Explanation of Solution

Given information: $\angle T$ is complement to $\angle W,\angle X$ is complement to $\angle Z.$

  $\angle Z=\angle W$

Formula used: Subtraction property.

Proof: $\angle T$ is complement to $\angle W$ and $\angle X$ is complement to $\angle Z$ (given)

  $\therefore \angle T+\angle W={90}^{\circ }$ and $\angle X+\angle Z={90}^{\circ }$

  $\therefore \angle T+\angle W=\angle X+\angle Z$ (Each equals ${90}^{\circ }$ )

  $\therefore \angle T+\angle W=\angle X+\angle W$ ( $\because \angle Z=\angle W$ )

  $\therefore \angle T=\angle X$ (Subtraction property).