Question

find the measure of the unknown angle

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
In triangle \(RQP\), \(\angle PGQ\) (the unknown angle) is an exterior angle. The two non - adjacent interior angles are \(\angle R = 35^{\circ}\) and \(\angle RQP=95^{\circ}\).

Step2: Calculate the measure of the unknown angle

By the exterior - angle theorem, \(\angle PGQ=\angle R+\angle RQP\).
Substitute the values: \(\angle PGQ = 35^{\circ}+95^{\circ}\).

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Answer:

\(130^{\circ}\)