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jmc

prealgebra intermediate

Problem

In the diagram below, we have

\overline{S T} ∥ \overline{QR}

,

∠ P = 4 0^{\circ}

, and

∠ Q = 3 5^{\circ}

. Find the measure of

∠ S T R

in degrees.

problem

Solution

From

△ P QR

, we have

∠ R = 18 0^{\circ} - ∠ Q - ∠ P = 10 5^{\circ}

. Since

\overline{S T} ∥ \overline{QR}

, we have

∠ S T R = 18 0^{\circ} - ∠ R = 7 5^{\circ}

.

Final answer

75^\circ