Supplementary angles in a fixed ratio: Two angles are supplementary and are in the ratio 1 : 4. What is the measure of the smaller angle (in degrees)?

Introduction / Context:Supplementary angles sum to 180°. When given their ratio, distribute 180° proportionally to find each angle.

Given Data / Assumptions:

• Angles in ratio 1 : 4.
• Sum = 180°.

Concept / Approach:Let the angles be x and 4x. Then x + 4x = 180 ⇒ 5x = 180.

Step-by-Step Solution:x = 180 / 5 = 36°Larger angle = 144° (check: 36 + 144 = 180)

Verification / Alternative check:Ratio check: 36 : 144 = 1 : 4, as required.

Why Other Options Are Wrong:45° or 35° do not satisfy both the 1:4 ratio and 180° sum; 72° would be the smaller angle if the ratio were 2:3, not 1:4.

Common Pitfalls:Confusing complementary (90°) with supplementary (180°).

Final Answer:36 degree