Question

1. assume c || g and the measure of ∠6 is 108°.a. what is the measure of ∠1?b. describe a sequence of rigid motions that verifies the measure of ∠1.c. what is the measure of ∠3?d. describe a sequence of rigid motions that verifies the measure of ∠3.5. would your answers to problem 3 be the same if lines c and g were not parallel? why?6. assume lines c and g are not parallel. explain why the measure of ∠2 is not equal to the measure of ∠7.

Explanation:

Step1: Use properties of parallel lines and transversals

Since \(c\parallel g\), \(\angle6\) and \(\angle1\) are supplementary (consecutive interior angles). So \(m\angle1 = 180^{\circ}-m\angle6\).

Step2: Calculate \(m\angle1\)

Substitute \(m\angle6 = 108^{\circ}\) into the formula: \(m\angle1=180^{\circ}- 108^{\circ}=72^{\circ}\).

Step3: Use vertical - angle property for \(\angle3\)

\(\angle3\) and \(\angle6\) are vertical angles. Vertical angles are equal. So \(m\angle3=m\angle6\).

Step4: Calculate \(m\angle3\)

Substitute \(m\angle6 = 108^{\circ}\) into the formula: \(m\angle3 = 108^{\circ}\).

Answer:

a. \(72^{\circ}\)
c. \(108^{\circ}\)