Question

given: a||b
find: the measure of <a, <b, <c, <d, <e, and <f

Explanation:

Step1: Find the measure of ∠A

∠A and \(66^{\circ}\) are vertical angles. Vertical angles are equal.
\(\angle A = 66^{\circ}\)

Step2: Find the measure of ∠B

\(\angle B\) and \(66^{\circ}\) are supplementary angles (they form a linear - pair). The sum of supplementary angles is \(180^{\circ}\).
\(\angle B=180^{\circ}- 66^{\circ}=114^{\circ}\)

Step3: Find the measure of ∠C

\(\angle C\) and \(66^{\circ}\) are alternate - interior angles. Since \(a\parallel b\), alternate - interior angles are equal.
\(\angle C = 66^{\circ}\)

Step4: Find the measure of ∠D

\(\angle D\) and \(\angle B\) are corresponding angles. Since \(a\parallel b\), corresponding angles are equal.
\(\angle D=\angle B = 114^{\circ}\)

Step5: Find the measure of ∠E

\(\angle E\) and \(66^{\circ}\) are corresponding angles. Since \(a\parallel b\), corresponding angles are equal.
\(\angle E = 66^{\circ}\)

Step6: Find the measure of ∠F

\(\angle F\) and \(27^{\circ}\) are vertical angles. Vertical angles are equal.
\(\angle F = 27^{\circ}\)

Answer:

\(\angle A = 66^{\circ}\), \(\angle B = 114^{\circ}\), \(\angle C = 66^{\circ}\), \(\angle D = 114^{\circ}\), \(\angle E = 66^{\circ}\), \(\angle F = 27^{\circ}\)