Delta PQR sim Delta XYZ for the correspondenc | vedclass

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Question

(B) Given the correspondence $PQR \leftrightarrow YZX$ is a similarity,the corresponding angles are equal.Therefore,$m \angle P = m \angle Y$,$m \angl

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(B) Given the correspondence $PQR \leftrightarrow YZX$ is a similarity,the corresponding angles are equal.Therefore,$m \angle P = m \angle Y$,$m \angle Q = m \angle Z$,and $m \angle R = m \angle X$.Given $m \angle X = 120^\circ$,it follows that $m \angle R = 120^\circ$.In $\Delta PQR$,the sum of angles is $m \angle P + m \angle Q + m \angle R = 180^\circ$.Substituting the given values: $m \angle P + m \angle Q + 120^\circ = 180^\circ$,which implies $m \angle P + m \angle Q = 60^\circ$.Since $m \angle P = 2 m \angle Q$,we substitute $m \angle P$ in the equation: $2 m \angle Q + m \angle Q = 60^\circ$.$3 m \angle Q = 60^\circ \implies m \angle Q = 20^\circ$.Then,$m \angle P = 2 	imes 20^\circ = 40^\circ$.Since $m \angle Y = m \angle P$,we have $m \angle Y = 40^\circ$.

$\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow YZX$. If $m \angle P = 2 m \angle Q$ and $m \angle X = 120^\circ$,then $m \angle Y = \dots$ (in $^\circ$)

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