Two Angles are Supplementary. One is 110°. Find the Other.
The Question
Two angles are supplementary. One angle measures 110°. Find the other angle.
What Are Supplementary Angles?
Two angles are supplementary if their sum equals 180°.
A straight line forms an angle of 180°. Any two angles that together make a straight line are supplementary.
Examples:
- 90° and 90° are supplementary (90 + 90 = 180)
- 120° and 60° are supplementary (120 + 60 = 180)
- 150° and 30° are supplementary (150 + 30 = 180)
Angle A and Angle B are supplementary if: A + B = 180°
Supplement of A = 180° − A
Solution
Let the other angle = x.
Since the two angles are supplementary:
110° + x = 180°
Transpose 110° to the right:
x = 180° - 110°
x = 70°
Check: 110° + 70° = 180° ✓
Visualising on a Straight Line
When two angles form a linear pair (on a straight line), they are supplementary.
110° 70°
_____________________The 110° and 70° together make a straight angle (180°).
Every linear pair is supplementary, but not every pair of supplementary angles needs to be a linear pair. The angles just need to add up to 180° — they can be far apart from each other on the page.
Common mistake: Subtracting from 90° instead of 180°.
If both angles are supplementary, subtract from 180°. If both angles are complementary, subtract from 90°.
110° is already greater than 90°, so it CAN’T have a complement (you’d get a negative number). It can only have a supplement.
Can Both Supplementary Angles Be Obtuse?
An obtuse angle is greater than 90°. If both supplementary angles were obtuse (both > 90°), their sum would be greater than 180°. But supplementary angles add to exactly 180°. So it’s impossible for both to be obtuse.
In a supplementary pair, at most one angle can be obtuse (or right). The other must be acute (or right).
Try These Similar Problems
Problem 1: Find the supplement of 75°.
Supplement = 180° - 75° = 105° Check: 75° + 105° = 180° ✓
Problem 2: Two supplementary angles are in the ratio 2:7. Find both angles.
Let the angles be 2k and 7k. 2k + 7k = 180° 9k = 180° k = 20°
Angles are 2(20°) = 40° and 7(20°) = 140°. Check: 40° + 140° = 180° ✓
Problem 3: An angle is 30° less than twice its supplement. Find the angle.
Let the angle = x. Its supplement = 180° - x.
Given: x = 2(180° - x) - 30° x = 360° - 2x - 30° x + 2x = 330° 3x = 330° x = 110°
The angle is 110° and its supplement is 70°. Check: 110° + 70° = 180° ✓, and 2(70°) - 30° = 140° - 30° = 110° ✓
Exam tip: Supplementary angle questions often appear alongside linear pair problems. Remember: a linear pair is ALWAYS supplementary (they’re on a straight line), but supplementary angles are not always a linear pair (they don’t have to be adjacent). This distinction is a common exam question.