Question

for problems 7 - 9, find the missing angle. 7) m∠abd = 60° m∠abc = _ 8) m∠wxy = 74° m∠wxz = _ 9) m∠pqr = ___

Explanation:

Step1: Recall angle - addition property

The measure of an angle formed by two non - collinear rays with a common endpoint is the sum of the measures of the non - overlapping angles with the same common endpoint.

Step2: Solve for problem 7

We know that \(m\angle ABD = 60^{\circ}\) and one part of \(\angle ABD\) is \(32^{\circ}\). Let \(m\angle ABC=x\). Then \(x + 32^{\circ}=60^{\circ}\), so \(x=m\angle ABC=60^{\circ}- 32^{\circ}=28^{\circ}\).

Step3: Solve for problem 8

We know that \(m\angle WXY = 74^{\circ}\) and one part of \(\angle WXY\) is \(41^{\circ}\). Let \(m\angle WXZ = y\). Then \(y+41^{\circ}=74^{\circ}\), so \(y = m\angle WXZ=74^{\circ}-41^{\circ}=33^{\circ}\).

Step4: Solve for problem 9

We know that the sum of the non - overlapping angles \(\angle PQS\) and \(\angle SQR\) form \(\angle PQR\). \(\angle PQS = 60^{\circ}\) and \(\angle SQR=27^{\circ}\), so \(m\angle PQR=60^{\circ}+27^{\circ}=87^{\circ}\).

Answer:

1. \(28^{\circ}\)
2. \(33^{\circ}\)
3. \(87^{\circ}\)