If △ ABC ~ △ DEF and ∠ A = 47°, ∠ E = 83°, then ∠ C is equal: (A) 47° (B) 50° (C) 83° (D) 130°

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2023: question 8

Set in the CBSE Class 10 board exam of 2023, paper 430/4/1, section A, question 8, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q8 · 1 mark · MCQTriangles

If $△ A B C \sim △ D E F$ and $∠ A = 4 7^{\circ}$ , $∠ E = 8 3^{\circ}$ , then $∠ C$ is equal:

(A) $4 7^{\circ}$
(B) $5 0^{\circ}$
(C) $8 3^{\circ}$
(D) $13 0^{\circ}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/4/1.

Hints

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

Hint 1

Which angle of $△ A B C$ corresponds to $∠ E$ ?

Hint 2

Use the fact that the angles of a triangle add up to $18 0^{\circ}$ .

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.

In similar triangles, corresponding angles are equal, so $∠ B = ∠ E = 8 3^{\circ}$ .
By the angle sum property, $∠ C = 18 0^{\circ} - 4 7^{\circ} - 8 3^{\circ} = 5 0^{\circ}$ . Answer: option (B).
1 mark

Answer: $5 0^{\circ}$ , option (B)

Where the marks are

Uses $∠ B = ∠ E$ and the angle sum property to get $5 0^{\circ}$ (1 mark)

Revise the chapter

Chapter: Triangles (notes, formulas, where marks are lost and every past question)
Topic: AAA and AA Similarity Criterion

Practise this chapterBoard-style questions from Triangles, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 430/4/1 (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 2023: question 8

Hints

Step-by-step solution

Revise the chapter

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