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.
Generated by claude-sonnet-4-6 · 2026-06-15 10:35 · grounding rag
Model Answer
Let the greater angle = x° and the smaller angle = y°.
Since the angles are supplementary:
$$x + y = 180 \quad \text{...(1)}$$
Since the greater exceeds the smaller by 50°:
$$x - y = 50 \quad \text{...(2)}$$
Adding (1) and (2): $2x = 230 \Rightarrow x = 115°$
Substituting in (1): $y = 180 - 115 = 65°$
The greater angle is 115° and the smaller angle is 65°.
Source: Chapter 3, Pair of Linear Equations in Two Variables
---
Explanation
- 1 mark for correctly forming both equations; 1 mark for solving and stating the answer.
- Supplementary angles sum to 180° — this gives equation (1). The word "exceeds by" means difference — this gives equation (2).
- Adding the two equations is the quickest elimination step; show it clearly.
- Always state the final answer in a sentence for full credit.