If ΔPQR ~ ΔXYZ and ∠X= 30°, ∠Q=50°, then ∠Z = ………… If ΔPQR ~ ΔXYZ and ∠X= 30°, ∠Q = 50°, then ∠Z = …………

Correct option is (C) Both A and B

Given that \(\triangle PQR\sim\triangle XYZ\)

\(\therefore\) \(\angle P=\angle X,\)

\(\angle Q=\angle Y\) and

\(\angle R=\angle Z\)

\(\therefore\) \(\angle Y=\angle Q\) \(=50^\circ\)

Now in \(\triangle XYZ,\) we have

\(\angle X+\angle Y+\angle Z=180^\circ\)       (Sum of angles in a triangle)

\(\Rightarrow\) \(30^\circ+50^\circ+\angle Z=180^\circ\)   \((\because\angle X=30^\circ\;\&\;\angle Y=50^\circ)\)

\(\Rightarrow\) \(\angle Z=180^\circ-80^\circ=100^\circ\)

\(\therefore\) \(\angle Z=100^\circ\) \(and\;\angle Z=\angle R\)

Correct option is: (C) both A and B