In the given figure, △ OSR ~ △ OQP, ∠ ROQ = 125° and ∠ ORS = 70°. Find the measures of ∠ OSR and ∠ OQP.

MathsCBSE Class 10 · Basic · Board exam 2026, set 430/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 22(b)

Set in the CBSE Class 10 board exam of 2026, paper 430/1/1, section B, question 22(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(b) · 2 marks · Very short answerTriangles

In the given figure, $△ O S R \sim △ O QP$ , $∠ R O Q = 12 5^{\circ}$ and $∠ O R S = 7 0^{\circ}$ . Find the measures of $∠ O S R$ and $∠ O QP$ .

Figure in the paper: Two parallel horizontal lines: S and R on the upper line, P and Q on the lower line. Segments SQ and RP cross at O. Angle ORS = 70° marked at R; angle ROQ = 125° marked at O. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

The angles $∠ R O Q$ and $∠ S O R$ lie on the straight line SQ.

Hint 2

After finding $∠ S O R$ , use the angle sum of $△ O S R$ .

Hint 3

In similar triangles, corresponding angles are equal. Match S with Q.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

$S$ , $O$ , $Q$ are collinear, so $∠ S O R = 18 0^{\circ} - ∠ R O Q = 18 0^{\circ} - 12 5^{\circ} = 5 5^{\circ}$ [linear pair].
½ mark
In $△ O S R$ : $∠ O S R = 18 0^{\circ} - (∠ S O R + ∠ O R S) = 18 0^{\circ} - (5 5^{\circ} + 7 0^{\circ}) = 5 5^{\circ}$ [angle sum property].
1 mark
Since $△ O S R \sim △ O QP$ , corresponding angles are equal: $∠ O QP = ∠ O S R = 5 5^{\circ}$ .
½ mark

Answer: $∠ O S R = 5 5^{\circ}$ , $∠ O QP = 5 5^{\circ}$

Where the marks are

Finds $∠ S O R = 5 5^{\circ}$ using linear pair (½ mark)
Finds $∠ O S R = 5 5^{\circ}$ by angle sum property (1 mark)
Uses similarity to get $∠ O QP = 5 5^{\circ}$ (½ mark)

Revise the chapter

Chapter: Triangles (notes, formulas, where marks are lost and every past question)
Topic: Problems on Similar Triangles

Practise this chapterBoard-style questions from Triangles, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 430/1/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Basic 2026: question 22(b)

Hints

Step-by-step solution

Revise the chapter

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