Fundamental relationships between pairs of angles: supplementary angles sum to 180°, complementary angles sum to 90°, vertical angles are equal, and adjacent angles share a common ray.
Think of opening a book flat on a table—the two pages form supplementary angles (they add to a straight line, 180°). Now think of the corner of a room where two walls meet the floor—those two angles are complementary (they add to a right angle, 90°). When two lines cross like an X, the opposite angles are always equal—those are vertical angles.
Showing a random 20 of 50 problems.
Example 1
easy
Can two obtuse angles be supplementary?
Example 2
easy
Two angles are supplementary. One is 43°. Find the other.Supplementary angles: find x when one angle is 43°
Example 3
medium
Why are vertical angles always equal?
Example 4
medium
Ray OB bisects angle AOC. If angle AOC = 76°, find angle AOB.
Example 5
medium
Angle A and angle B are complementary. Angle A is twice angle B. Find both.
Example 6
medium
Two angles form a linear pair. The supplement is four times the angle. Find both.
Example 7
easy
Two adjacent angles form a right angle. One is 37°. Find the other.
Example 8
medium
An angle's supplement is 40° more than twice its complement. Find the angle.
Example 9
challenge
Two adjacent angles form a straight line. The angle bisectors of each form a new angle between them. Prove that this new angle is always 90°.
Example 10
medium
Two angles are supplementary, and their measures are in the ratio 7:5. Find both angles.
Example 11
challenge
Two angles are supplementary. The larger exceeds three times the smaller by 20°. Find both angles.
Example 12
easy
Two angles are supplementary. One is 110°. Find the other.Supplementary angles on a straight line; find x
Example 13
easy
Two angles are complementary. One is 35°. Find the other.
Example 14
easy
Two angles are supplementary and one is a right angle. Find the other.
Example 15
medium
Two lines intersect forming four angles. One angle is 124°. Find all four angles.
Example 16
easy
An angle is equal to its own complement. Find the angle.
Example 17
medium
Two supplementary angles are in the ratio 2:7. Find the larger angle.
Example 18
challenge
On a clock, find the angle between the hour and minute hands at 3:30.
Example 19
easy
Two angles are complementary. One is 28°. Find the other.
Example 20
medium
Two vertical angles measure (5x−12)° and (3x+8)°. Find x and each angle.