Question

One of the supplementary angles exceeds the other by 120°. Express this as a system of linear equations and find the angles.

Hint:

"Supplementary" means sum to 180°, while "Complementary" means sum to 90°. A quick way to remember: 'C' comes before 'S', and 90 comes before 180.

Answer 1

Step 1: Solving OR (B):
1. Let the two angles be \(x\) and \(y\).
2. Supplementary angles sum to 180°: \(x + y = 180\)
3. Given condition: \(x - y = 120\)
4. Adding the two equations: \(2x = 300 \implies x = 150^\circ\).
5. Substituting \(x\): \(150 + y = 180 \implies y = 30^\circ\).
Step 2: Final Answer (OR):
The system is \(x+y=180, x-y=120\). The angles are 150° and 30°.