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The measures of two complementary angles are in the ratio 1 : 5. How many degrees is the larger of the two?

Class 7Lines and AnglesLines and Angles
  • A15°
  • B150°
  • C75°
  • D72°

Step-by-Step Solution

Complementary angles sum to 90°. The parts total 1 + 5 = 6, so one part = 90 ÷ 6 = 15°. The angles are 15° and 75°, and the larger is 75°. Trap: 15° is the smaller angle; 150° comes from splitting 180° instead of 90°, which is the SUPPLEMENTARY rule applied to a complementary pair.
Answer: C) 75°

Key idea: Complementary and supplementary

Two angles are **complementary** if they add to 90°. So if one is 35°, the complement is 90° − 35° = 55°.

Two angles are **supplementary** if they add to 180°. So if one is 110°, the supplement is 180° − 110° = 70°.

The angles don't have to be next to each other — only their measures matter.

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