Question

1. 23) find the measure of the angle indicated in bold. 25) 27)

Explanation:

Step1: Use the property of parallel lines and transversal (for problem 25)

When two parallel lines are cut by a transversal, the sum of consecutive interior angles on the same side of the transversal is \(180^{\circ}\). But in this case, since the two angles \(x + 96\) and \(x+96\) are formed by two parallel lines and a transversal (vertical line), and they are supplementary (they form a linear - pair with the angles between the parallel lines). So, \((x + 96)+(x + 96)=180\).

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Step2: Find the angle measure (for problem 25)

Substitute \(x=-6\) into \(x + 96\). The angle measure is \(-6+96 = 90^{\circ}\)

Step3: Use the property of parallel lines and transversal (for problem 27)

When two parallel lines are cut by a transversal, the alternate - interior angles are equal. So, \(6x=5x + 10\)

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Step4: Find the angle measure (for problem 27)

Substitute \(x = 10\) into \(6x\). The angle measure is \(6\times10=60^{\circ}\)

Answer:

For problem 25: \(90^{\circ}\)
For problem 27: \(60^{\circ}\)