Practice Angles in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The amount of rotation between two rays that share a common endpoint, measured in degrees or radians.

Opening a door wider makes a bigger angle; a corner of a book is 90°90°.

Showing a random 20 of 50 problems.

Example 1

medium
A clock shows 4:004:00. What is the smaller angle between the hour and minute hands?

Example 2

easy
An angle measures 89∘89^\circ. Is it acute, right, or obtuse?

Example 3

hard
At what time between 3:003:00 and 4:004:00 are the clock's hands first perpendicular?

Example 4

medium
An angle is its own supplement. Find the angle.

Example 5

hard
At 9:009{:}00 the hour hand starts moving. How many degrees has it rotated by 9:409{:}40?

Example 6

easy
An angle measures 45∘45^\circ. Is it acute, right, or obtuse?

Example 7

challenge
At 3:30, what is the angle between the hour and minute hands?

Example 8

easy
A clock's hands point at 3:00. What angle do they make?

Example 9

medium
Two angles are supplementary and in the ratio 2:32:3. Find the larger angle.

Example 10

hard
The complement of an angle is 14\tfrac{1}{4} of its supplement. Find the angle.

Example 11

medium
Two parallel lines are cut by a transversal. Alternate exterior angles measure (4x+5)∘(4x + 5)^\circ and (6x−25)∘(6x - 25)^\circ. Find each angle.

Example 12

easy
Two angles are supplementary. One measures 115°115°. Find the other.

Example 13

easy
Two angles add to 90∘90^\circ. What are they called?

Example 14

easy
Two angles together form a right angle. One is 30∘30^\circ. What is the other?

Example 15

medium
The supplement of an angle is 40∘40^\circ less than three times its complement. Find the angle.

Example 16

challenge
Two lines cross. The angles are in the ratio 1:1:1:11:1:1:1 in one figure and 2:7:2:72:7:2:7 in another. Which figure is possible, and what are its angles?

Example 17

easy
An angle is 120∘120^\circ. Acute, right, or obtuse?

Example 18

easy
How many degrees are in a straight angle?

Example 19

medium
Two parallel lines are cut by a transversal. One of the alternate interior angles measures 72°72°. Find all eight angles formed.

Example 20

hard
Three rays from a point divide the plane into three angles in the ratio 2:3:52:3:5. Find each angle.
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