Question

find the measure of each numbered angle.

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Explanation:

Step1: Find \(m\angle2\)

In \(\triangle UR V\), use the triangle - angle sum theorem (\(m\angle2+35^{\circ}+80^{\circ}=180^{\circ}\)).

$$m\angle2 = 180^{\circ}-(35^{\circ}+80^{\circ})=65^{\circ}$$

Step2: Find \(m\angle1\)

\(\angle1\) and \(\angle2\) are vertical angles. Vertical angles are equal. So \(m\angle1 = m\angle2 = 65^{\circ}\).

Step3: Find \(m\angle3\)

\(\angle1\) and \(\angle3\) are supplementary (they form a linear pair). So \(m\angle1 + m\angle3=180^{\circ}\).

$$m\angle3=180^{\circ}-m\angle1 = 180^{\circ}-65^{\circ}=115^{\circ}$$

Answer:

\(m\angle1 = 65^{\circ}\), \(m\angle2 = 65^{\circ}\), \(m\angle3 = 115^{\circ}\)