Find the Complement of 35°
The Question
Find the complement of 35°.
What Are Complementary Angles?
Two angles are complementary if their sum equals 90°.
Think of a right angle (the corner of a square). If we split it into two parts, each part is the complement of the other.
Examples:
- 30° and 60° are complementary (30 + 60 = 90)
- 45° and 45° are complementary (45 + 45 = 90)
- 80° and 10° are complementary (80 + 10 = 90)
Angle A and Angle B are complementary if: A + B = 90°
Complement of A = 90° − A
Solution
We need the complement of 35°.
Using the formula:
Complement = 90° - 35°
Complement = 55°
Check: 35° + 55° = 90° ✓
Visualising It
Imagine a right angle (90°). Place a 35° angle inside it. The remaining part is the complement.
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|← 55° →|← 35° →
_________|_________________
(Right angle = 90°)The 35° and 55° together make the full right angle.
Complementary angles don’t have to be adjacent (next to each other). They can be in completely different places — as long as they add up to 90°, they are complementary.
Common mistake: Finding the supplement (180° - 35° = 145°) instead of the complement (90° - 35° = 55°).
Complementary = adds to 90° (think: “C” for Corner, i.e., right angle corner). Supplementary = adds to 180° (think: “S” for Straight angle).
Try These Similar Problems
Problem 1: Find the complement of 60°.
Complement = 90° - 60° = 30° Check: 60° + 30° = 90° ✓
Problem 2: Find the complement of 45°.
Complement = 90° - 45° = 45° Check: 45° + 45° = 90° ✓
(An angle and its own complement are equal when the angle is 45°!)
Problem 3: An angle is 20° more than its complement. Find the angle.
Let the angle = x. Its complement = 90° - x.
Given: x = (90° - x) + 20° x = 110° - x 2x = 110° x = 55°
The angle is 55° and its complement is 35°. Check: 55° - 35° = 20° ✓ and 55° + 35° = 90° ✓
Exam tip: Complement questions are easy marks — just subtract from 90°. But watch out for word problems like “an angle is twice its complement.” These need a small equation to solve. Practice both types.