In a pair of supplementary angles, the greater angle exceeds the smaller by 50°. Express the given situation as a system of linear equations in two variables and hence obtain the measure of each angle.

Equations: x + y = 180, y - x = 50; angles 65° and 115°

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 21(b)

Set in the CBSE Class 10 board exam of 2025, paper 30/6/1, section B, question 21(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(b) · 2 marks · Very short answerCompetency-basedPair of Linear Equations in Two Variables

In a pair of supplementary angles, the greater angle exceeds the smaller by $5 0^{\circ}$ . Express the given situation as a system of linear equations in two variables and hence obtain the measure of each angle.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/6/1.

Hints

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

Hint 1

Supplementary angles add up to $18 0^{\circ}$ .

Hint 2

Write one equation for the sum and one for the difference, then add them.

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.

Let the smaller angle be $x^{\circ}$ and the greater angle be $y^{\circ}$ . Since they are supplementary: $x + y = 180$ ...(1)
½ mark
The greater exceeds the smaller by $5 0^{\circ}$ : $y - x = 50$ ...(2)
½ mark
Adding (1) and (2): $2 y = 230 \Rightarrow y = 115$
½ mark
From (1): $x = 180 - 115 = 65$ . So the angles are $6 5^{\circ}$ and $11 5^{\circ}$ .
½ mark

Answer: Equations: $x + y = 180$ , $y - x = 50$ ; angles $6 5^{\circ}$ and $11 5^{\circ}$

Where the marks are

Forms $x + y = 180$ (½ mark)
Forms $y = x + 50$ (½ mark)
Finds smaller angle $6 5^{\circ}$ (½ mark)
Finds greater angle $11 5^{\circ}$ (½ mark)

Revise the chapter

Chapter: Pair of Linear Equations in Two Variables (notes, formulas, where marks are lost and every past question)
Topic: Word Problems on Linear Equations

Practise this chapterBoard-style questions from Pair of Linear Equations in Two Variables, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 30/6/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 21(b)

Hints

Step-by-step solution

Revise the chapter

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