Question

question. type the correct answer in the boxes provided. find the measure of the missing angles. m∠a degrees m∠b degrees m∠c degrees m∠d degrees m∠e degrees

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle \(e\) and the \(70^{\circ}\) angle are vertical angles, so \(m\angle e=70^{\circ}\).

Step2: Use linear - pair property

A linear - pair of angles sums to \(180^{\circ}\). Angle \(d\) and angle \(e\) form a linear pair. So \(m\angle d = 180 - 70=110^{\circ}\).

Step3: Use vertical - angle property again

Angle \(c\) and angle \(d\) are vertical angles, so \(m\angle c=m\angle d = 110^{\circ}\).

Step4: Assume the right - angle

If we assume the unlabeled angle next to \(b\) is a right - angle (\(90^{\circ}\)). Angle \(b\) and the \(70^{\circ}\) angle and the right - angle are on a straight line. So \(m\angle b=180-(90 + 70)=20^{\circ}\).

Step5: Use vertical - angle property for angle \(a\)

Angle \(a\) and angle \(b\) are vertical angles, so \(m\angle a=m\angle b = 20^{\circ}\).

Answer:

\(m\angle a = 20\) degrees
\(m\angle b = 20\) degrees
\(m\angle c = 110\) degrees
\(m\angle d = 110\) degrees
\(m\angle e = 70\) degrees