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

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 22(b)

Set in the CBSE Class 10 board exam of 2025, 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 (SR), P and Q on the lower line (PQ). Segments SQ and RP cross at O. Angle at R between RS and RO marked 70°. Angle ROQ = 125° marked at O on the right side. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/1/1.

Hints

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

Hint 1

$∠ R O Q$ lies outside $△ O R S$ and stands on the straight line SQ.

Hint 2

An exterior angle equals the sum of the two interior opposite angles. Then match the vertices of the similar triangles in order.

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.

SOQ is a straight line, so $∠ R O Q$ is an exterior angle of $△ O R S$ . Then $∠ R O Q = ∠ O R S + ∠ O S R$ [exterior angle property], so $12 5^{\circ} = 7 0^{\circ} + ∠ O S R$ , giving $∠ O S R = 5 5^{\circ}$ .
1 mark
Since $△ O S R \sim △ O QP$ with $S \leftrightarrow Q$ , we get $∠ O QP = ∠ O S R$ [corresponding angles of similar triangles].
½ mark
$∴ ∠ O QP = 5 5^{\circ}$ .
½ mark

Answer: ∠OSR = 55°, ∠OQP = 55°

Where the marks are

Uses the exterior angle property to get $∠ O S R = 5 5^{\circ}$ (1 mark)
States that corresponding angles of similar triangles are equal (½ mark)
Concludes $∠ O QP = 5 5^{\circ}$ (½ mark)

Revise the chapter

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

Practise this chapterBoard-style questions from Triangles, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 430/1/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 22(b)

Hints

Step-by-step solution

Revise the chapter

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