Angles in circles word problems Our mission is to provide a free, world-class education to anyone, anywhere. Khan Academy is a 501(c)(3) nonprofit organization. So, the required angle is 60°. Problem 6: Two angles are supplementary. If 5 times of one angle is 10 times of the other angle. Find the two angles. Solution: Let x and y be the two angles which are supplementary. Then, x + y = 180 -(1) Given: 5 times of one angle is 10 times of the other angle. Divide each side by 5.
An angle measures the amount of turn
Names of Angles
As the Angle Increases, the Name Changes:
| Type of Angle | Description |
|---|---|
| Acute Angle | is less than 90° |
| Right Angle | is 90° exactly |
| Obtuse Angle | is greater than 90° but less than 180° |
| Straight Angle | is 180° exactly |
| Reflex Angle | is greater than 180° |
| Full Rotation | is 360° exactly |
Try It Yourself:
In One DiagramThis diagram might make it easier to remember: Also: Acute, Obtuse and Reflex are in alphabetical order. |
Also: the letter 'A' has an acute angle.
Be Careful What You Measure
| The smaller angle is an Obtuse Angle, but the larger angle is a Reflex Angle |
So when naming the angles make sure that you know which angle is being asked for!
Positive and Negative Angles
When measuring from a line:
- a positive angle goes counterclockwise (opposite direction that clocks go)
- a negative angle goes clockwise
Parts of an Angle
The corner point of an angle is called the vertex
And the two straight sides are called arms
The angle is the amount of turn between each arm.
How to Label Angles
There are two main ways to label angles:
1. give the angle a name, usually a lower-case letter like a or b, or sometimes a Greek letter like α (alpha) or θ (theta)
2. or by the three letters on the shape that define the angle, with the middle letter being where the angle actually is (its vertex).
Example angle 'a' is 'BAC', and angle 'θ' is 'BCD'
An angle measures the amount of turn
Names of Angles
As the Angle Increases, the Name Changes:
| Type of Angle | Description |
|---|---|
| Acute Angle | is less than 90° |
| Right Angle | is 90° exactly |
| Obtuse Angle | is greater than 90° but less than 180° |
| Straight Angle | is 180° exactly |
| Reflex Angle | is greater than 180° |
| Full Rotation | is 360° exactly |
Try It Yourself:
In One DiagramThis diagram might make it easier to remember: Also: Acute, Obtuse and Reflex are in alphabetical order. |
Also: the letter 'A' has an acute angle.
Be Careful What You Measure
| The smaller angle is an Obtuse Angle, but the larger angle is a Reflex Angle |
So when naming the angles make sure that you know which angle is being asked for!
Positive and Negative Angles
When measuring from a line:
- a positive angle goes counterclockwise (opposite direction that clocks go)
- a negative angle goes clockwise
Parts of an Angle
The corner point of an angle is called the vertex
And the two straight sides are called arms
The angle is the amount of turn between each arm.
How to Label Angles
There are two main ways to label angles:
Vertical Angles Problem Solving
1. give the angle a name, usually a lower-case letter like a or b, or sometimes a Greek letter like α (alpha) or θ (theta)
Steps In Math Problem Solving
2. or by the three letters on the shape that define the angle, with the middle letter being where the angle actually is (its vertex).
Example angle 'a' is 'BAC', and angle 'θ' is 'BCD'