Question

find the measure of the missing angles.

Explanation:

Step1: Find angle \( d \)

Vertical angles are equal, so \( d = 22^\circ \) (since the \( 22^\circ \) angle and \( d \) are vertical angles).

Step2: Find angle \( f \)

We know that a straight line is \( 180^\circ \). The angle of \( 114^\circ \), \( d = 22^\circ \), and \( f \) are on a straight line. So we can calculate \( f \) as:
\( f = 180^\circ - 114^\circ - 22^\circ \)
\( f = 44^\circ \)

Step3: Find angle \( e \)

Vertical angles are equal, so \( e = 114^\circ \) (since the \( 114^\circ \) angle and \( e \) are vertical angles).

Answer:

\( d = 22^\circ \), \( e = 114^\circ \), \( f = 44^\circ \)