Question

(provide all theorems / reasoning and show all work**)
given: ( aparallel b )
find: the measure of ( angle a,angle b,angle c,angle d,angle e ), and ( angle f )
( angle a=)
( angle b=)
( angle c=)
( angle d=)
( angle e=)
( angle f=)

Explanation:

Step1: Find \(\angle A\)

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

Step2: Find \(\angle B\)

\(\angle B\) and \(66^{\circ}\) are vertical angles. So \(\angle B=66^{\circ}\)

Step3: Find \(\angle C\)

Sum of angles around a point is \(180^{\circ}\). \(\angle C = 180^{\circ}-\angle A-\angle B\). Substitute \(\angle A = 27^{\circ}\) and \(\angle B = 66^{\circ}\). \(\angle C=180^{\circ}-27^{\circ}-66^{\circ}=87^{\circ}\)

Step4: Find \(\angle D\)

\(\angle D\) and \(\angle C\) are alternate - interior angles (since \(a\parallel b\)). Alternate - interior angles are equal. So \(\angle D = 87^{\circ}\)

Step5: Find \(\angle E\)

\(\angle E\) and \(66^{\circ}\) are alternate - interior angles (since \(a\parallel b\)). Alternate - interior angles are equal. So \(\angle E = 66^{\circ}\)

Step6: Find \(\angle F\)

\(\angle F\) and \(27^{\circ}\) are alternate - interior angles (since \(a\parallel b\)). Alternate - interior angles are equal. So \(\angle F = 27^{\circ}\)

Answer:

\(\angle A = 27^{\circ}\)
\(\angle B = 66^{\circ}\)
\(\angle C = 87^{\circ}\)
\(\angle D = 87^{\circ}\)
\(\angle E = 66^{\circ}\)
\(\angle F = 27^{\circ}\)