Question

4pts: find each missing angle below

Explanation:

Step1: Find angle \( a \)

Use the property of parallel lines and transversal (corresponding angles).
\( a = 78^{\circ} \)

Step2: Find angle \( b \)

Use the property of supplementary angles (\( a + b=180^{\circ} \)).
\( b = 180^{\circ}-78^{\circ}=102^{\circ} \)

Step3: Find angle \( f \)

Use the property of vertical angles (vertical angles are equal).
\( f = 44^{\circ} \)

Step4: Find angle \( e \)

Use the triangle - angle sum property (sum of angles in a triangle is \( 180^{\circ} \), and there is a right - angle \( 90^{\circ} \)).
\( e=180^{\circ}-(90^{\circ}+64^{\circ}) = 26^{\circ} \)

Step5: Find angle \( c \)

Use the property of parallel lines and transversal (alternate interior angles).
\( c = e = 26^{\circ} \)

Step6: Find angle \( d \)

Use the property of vertical angles (vertical angles are equal).
\( d = 64^{\circ} \)

Answer:

\( a = 78^{\circ}\), \( b = 102^{\circ}\), \( c = 26^{\circ}\), \( d = 64^{\circ}\), \( e = 26^{\circ}\), \( f = 44^{\circ}\)