Chapter 2.1, Problem 4PSA

a)

To determine

To calculate: $\angle 2$

Answer to Problem 4PSA

  ${30}^{\circ }$

Explanation of Solution

Given information: $\angle 1=5\angle 2$

Formula Used: linear pair axiom

Calculation:

  $\begin{array}{l}\angle 1+\angle 2={180}^{\circ }(\text{Linear}\text{pair}\text{axiom})\\ 5\angle 2+\angle 2={180}^{\circ }\\ 6\angle 2={180}^{\circ }\\ \angle 2={30}^{\circ }\end{array}$

b)

To determine

To calculate: $m\angle 4$

Answer to Problem 4PSA

  $1^{\circ }13\text{'}25"$

Explanation of Solution

Given information: $\angle 3=72\angle 4,PQ\perp QR.$

Formula Used: linear pair axiom

Calculation:

  $\begin{array}{l}\because PQ\perp QR(given)\\ \therefore \angle PQR={90}^{\circ }\\ \therefore \angle 3+\angle 3={90}^{\circ }\\ \therefore 72\angle 4+\angle 4={90}^{\circ }\\ 73\angle 4={90}^{\circ }\\ \angle 4=1^{\circ }13\text{'}25"\end{array}$