CBSE2026Class Class 10 · Mathematics2 Marks · Short✅ Verified
In the given figure, $\triangle OSR \sim \triangle OQP$, $\angle ROQ=125^{\circ}$ and $\angle ORS=70^{\circ}$. Find the measures of $\angle OSR$ and $\angle OQP$. (In the figure, $S$ and $R$ lie on one line, $P$ and $Q$ lie on a parallel line, and the segments $SQ$ and $RP$ intersect at $O$.)
✅ Answer & Solution
Step 1: $R$, $O$ and $P$ are collinear, so $\angle SOR$ and $\angle ROQ$ form a linear pair.
$$\angle SOR+\angle ROQ=180^{\circ}$$
Step 2: Substitute $\angle ROQ=125^{\circ}$.
$$\angle SOR=180^{\circ}-125^{\circ}=55^{\circ}$$
Step 3: In $\triangle OSR$, use the angle sum property.
$$\angle OSR+\angle ORS+\angle SOR=180^{\circ}$$
$$\angle OSR+70^{\circ}+55^{\circ}=180^{\circ}$$
Step 4: Therefore
$$\angle OSR=180^{\circ}-125^{\circ}=55^{\circ}$$
Step 5: Since $\triangle OSR \sim \triangle OQP$, corresponding angles are equal with $S\leftrightarrow Q$.
$$\angle OQP=\angle OSR=55^{\circ}$$
Hence $\angle OSR=55^{\circ}$ and $\angle OQP=55^{\circ}$.
