Chapter 2.1, Problem 3PSA

a)

To determine

To Calculate: $\angle 1$ In each figure

Answer to Problem 3PSA

  ${21}^{\circ }42\text{'}26"$

Explanation of Solution

Given information: $AB\perp BC$ and $\angle 2={68}^{\circ }17\text{'}34"$

Calculation:

  $\because AB\perp BC$ Hence $\angle ABC={90}^{\circ }$

  $\therefore \angle 1+\angle 2={90}^{\circ }$

  $\therefore \angle 1={90}^{\circ }-\angle 2={90}^{\circ }-{68}^{\circ }17\text{'}34"$

  $\therefore \angle 1={21}^{\circ }42\text{'}26"$

b)

To determine

To Calculate: $\angle 1$ In each figure

Answer to Problem 3PSA

  ${45}^{\circ }$

Explanation of Solution

Given information: $DE\perp EF$ , EG bisects $\angle DEF$

Calculation:

  $\angle 1=\angle 2$ Hence $\angle ABC={90}^{\circ }$

Also, EG bisects $\angle DEF$ , hence $\angle 1=\angle 2$

  $\therefore \angle 1+\angle 2={90}^{\circ }$

  $\therefore \angle 1={45}^{\circ }$