If Delta ABC sim Delta PQR for the correspond | vedclass

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(B) Given the ratio of the angles in $\Delta ABC$ is $m \angle A : m \angle B : m \angle C = 2 : 3 : 5$.Let the angles be $2x, 3x,$ and $5x$.Since the

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$54$

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(B) Given the ratio of the angles in $\Delta ABC$ is $m \angle A : m \angle B : m \angle C = 2 : 3 : 5$.Let the angles be $2x, 3x,$ and $5x$.Since the sum of angles in a triangle is $180^{\circ}$,we have $2x + 3x + 5x = 180^{\circ}$.$10x = 180^{\circ} \implies x = 18^{\circ}$.Therefore,$m \angle A = 2(18^{\circ}) = 36^{\circ}$,$m \angle B = 3(18^{\circ}) = 54^{\circ}$,and $m \angle C = 5(18^{\circ}) = 90^{\circ}$.Given the similarity correspondence $ABC \leftrightarrow QRP$,the corresponding angles are equal.Thus,$m \angle A = m \angle Q$,$m \angle B = m \angle R$,and $m \angle C = m \angle P$.Since $m \angle B = 54^{\circ}$,it follows that $m \angle R = 54^{\circ}$.

If $\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow QRP$ and $m \angle A : m \angle B : m \angle C = 2 : 3 : 5$,then $m \angle R = \dots$ (in $^{\circ}$)

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