A problem by fred fan

Level 1

In the diagram shown, P QR is a straight line segment. The measure of ∠QSR is

35 25 40 30 45

Fred Fan by fred fan , 21, Canada

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2 solutions

By the exterior angle theorem, we have

75 = ∠ Q S R + 30 75=\angle QSR + 30

∠ Q S R = 75 − 30 = 4 5 ∘ \angle QSR = 75-30=\boxed{45^\circ}

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A straight line is 180 degrees. So angle SQR = 180 - 75 = 105 degrees. \text{A straight line is 180 degrees. So angle SQR = 180 - 75 = 105 degrees.} The sum of interior angles of a triangle is 180 degrees, so angle QSR = 180 - 105 - 30 = 45 degrees. \text{The sum of interior angles of a triangle is 180 degrees, so angle QSR = 180 - 105 - 30 = 45 degrees.}

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