In figure, if AD = 6 cm, DB = 9 cm, AE = 8 cm and EC = 12 cm and ∠ ADE = 48°. Find ∠ ABC.

MathsCBSE Class 10 · Basic · Sample paper, session 2023-24 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2023-24: question 22(b)

From the official CBSE sample question paper for 2023-24, 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 figure, if $A D = 6$ cm, $D B = 9$ cm, $A E = 8$ cm and $E C = 12$ cm and $∠ A D E = 4 8^{\circ}$ . Find $∠ A B C$ .

Figure in the paper: Triangle ABC with A at the top. D lies on side AB and E lies on side AC; DE is joined. Marked: AD = 6 cm, DB = 9 cm, AE = 8 cm, EC = 12 cm, and angle ADE = 48° at D. Angle ABC at B is marked. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Compare the ratios $\frac{A D}{D B}$ and $\frac{A E}{E C}$ .

Hint 2

Equal ratios mean DE is parallel to BC (converse of BPT). Which angle at B corresponds to $∠ A D E$ ?

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 $△ A B C$ : $\frac{A D}{D B} = \frac{6}{9} = \frac{2}{3}$ and $\frac{A E}{E C} = \frac{8}{12} = \frac{2}{3}$ , so $\frac{A D}{D B} = \frac{A E}{E C}$ .
1 mark
Therefore $D E ∥ B C$ [converse of BPT]. So $∠ A B C = ∠ A D E$ [corresponding angles], giving $∠ A B C = 4 8^{\circ}$ .
1 mark

Answer: $∠ A B C = 4 8^{\circ}$

Where the marks are

Shows $\frac{A D}{D B} = \frac{A E}{E C} = \frac{2}{3}$ (1 mark)
Concludes $D E ∥ B C$ by the converse of BPT, and $∠ A B C = 4 8^{\circ}$ as corresponding angles (1 mark)

Revise the chapter

Chapter: Triangles (notes, formulas, where marks are lost and every past question)
Topic: Basic Proportionality Theorem (Thales Theorem)

Practise this chapterBoard-style questions from Triangles, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2023-24 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2023-24: question 22(b)

Hints

Step-by-step solution

Revise the chapter

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