From the figures given below, which of the following is true about the measure of ∠ P ? (A) ∠ P = 60° (B) ∠ P = 80° (C) ∠ P = 40° (D) The measure of ∠ P cannot be determined

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2025: question 8

Set in the CBSE Class 10 board exam of 2025, paper 430/1/1, section A, question 8, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q8 · 1 mark · MCQTriangles

From the figures given below, which of the following is true about the measure of $∠ P$ ?

(A) $∠ P = 6 0^{\circ}$
(B) $∠ P = 8 0^{\circ}$
(C) $∠ P = 4 0^{\circ}$
(D)The measure of $∠ P$ cannot be determined

Figure in the paper: Two triangles side by side. Triangle ABC: AB = 3.8 cm, BC = 6 cm, AC = $33$ cm, angle at A = 80°, angle at B = 60°. Triangle PQR: PQ = 12 cm, PR = $63$ cm, QR = 7.6 cm, with P, Q, R as vertices (R at the top). 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

Check the ratios of the corresponding sides of the two triangles.

Hint 2

Match the vertex opposite the side 12 cm with the vertex opposite the side 6 cm.

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.

Compare the sides: $\frac{P Q}{B C} = \frac{12}{6} = 2$ , $\frac{P R}{A C} = \frac{6 3}{3 3} = 2$ , $\frac{QR}{A B} = \frac{7.6}{3.8} = 2$ . So $△ A B C \sim △ R QP$ by SSS, with $A \leftrightarrow R$ , $B \leftrightarrow Q$ , $C \leftrightarrow P$ .
$∠ C = 18 0^{\circ} - 8 0^{\circ} - 6 0^{\circ} = 4 0^{\circ}$ [angle sum property].
So $∠ P = ∠ C = 4 0^{\circ}$ [corresponding angles of similar triangles]. The answer is option (C).
1 mark

Answer: ∠P = 40°, option (C)

Where the marks are

Establishes similarity and gets ∠P = ∠C = 40° (1 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 8

Hints

Step-by-step solution

Revise the chapter

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