Given, △PQR≅△STU and ∠R=80∘ and ∠S=78∘, What is the measure of ∠Q? Enter your answer in the box
+177 According to the given statement, \(\triangle {\text{PQR}} \cong \triangle {\text{STU}}\). Corresponding angles of congruent triangles have equal measure. Therefore, since \(m \angle \text{S} = 78^{\circ}\), this means that \(m \angle \text{P} = 78^{\circ}\). By the widely known Triangle Sum Angle Theorem, the sum of the interior angles of the triangle equals 180 degrees.
\(m \angle {\text{P}} + m \angle {\text{Q}} + m \angle {\text{R}} = 180^{\circ} \\ 78^{\circ} + m \angle {\text{Q}} + 80^{\circ} = 180^{\circ} \\ 158^{\circ} + m \angle {\text{Q}} = 180^{\circ} \\ m \angle {\text{Q}} = 22^{\circ}\)
