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In these lessons, we will give a summary of the properties of the angles of a triangle.

### Property 1: Triangle Sum Theorem

The sum of the 3 angles in a triangle is always 180°.

**How to prove the Triangle Sum Theorem?**

The following video shows how to prove that the sum of the angles of a triangle is 180 degrees. (Triangle Sum Theorem)

**How to Find the Missing Angle in a Triangle Using the Triangle Sum Theorem?**

Step 1: Write out the equation by adding all the angles and making them equal to 180°.

Step 2: Solve for x.

Step 3: Substitute to find the missing angles.

### Property 2:

The sum of an interior angle and its adjacent exterior angle is 180°.

### Property 3: Exterior Angle Theorem

An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

**Exterior Angles of a Triangle**

Finding the Unknown Angle of a Triangle

Example:

1. Evaluate triangle abc, where a = 40° and b = 60°. What is the exterior angle to ∠acb?

2. Evaluate triangle abc, where a = 50° and b = 30°. What is the exterior angle to ∠acb?

2. Evaluate triangle abc, where a = 90° and b = 40°. What is the exterior angle to ∠acb?

**How to use the Exterior Angle Theorem to solve problems involving angles in a triangle?**

### Property 4:

An equilateral triangle has 3 equal angles that are 60° each.

An isosceles triangle has 2 equal angles, which are the angles opposite the 2 equal sides.

**How to Find the Missing Angle in an Isosceles Triangle?**
**Parallel Lines and the Triangle Angle-Sum Theorem**

More Geometry Lessons

Geometry Worksheets

Geometry Games

In these lessons, we will give a summary of the properties of the angles of a triangle.

- Triangle Sum Theorem - The sum of the 3 angles in a triangle is always 180°
- The sum of an interior angle and its adjacent exterior angle is 180°
- Exterior Angle Theorem - An exterior angle of a triangle is equal to the sum of the two opposite interior angles
- An equilateral triangle has 3 equal angles that are 60° each. An isosceles triangle has 2 equal angles, which are the angles opposite the 2 equal sides

The angles of a triangle have the following properties:

*Example : *

The following video shows how to prove that the sum of the angles of a triangle is 180 degrees. (Triangle Sum Theorem)

Step 1: Write out the equation by adding all the angles and making them equal to 180°.

Step 2: Solve for x.

Step 3: Substitute to find the missing angles.

* Example*

* Example*

Finding the Unknown Angle of a Triangle

Example:

1. Evaluate triangle abc, where a = 40° and b = 60°. What is the exterior angle to ∠acb?

2. Evaluate triangle abc, where a = 50° and b = 30°. What is the exterior angle to ∠acb?

2. Evaluate triangle abc, where a = 90° and b = 40°. What is the exterior angle to ∠acb?

An isosceles triangle has 2 equal angles, which are the angles opposite the 2 equal sides.

The above angle properties can help us to find unknown angles in a triangle.

* Example:*

Find the value of *x* in the following triangle.

* Solution: *

* x* + 24° + 32° = 180° (sum of angles is 180°)

*x* + 56° = 180°

*x* = 180° – 56° = 124°

** Example : **

Find the values of *x* and *y* in the following triangle.

* Solution: *

* x* + 50° = 92° (sum of opposite interior angles = exterior angle)

*x* = 92° – 50° = 42°

* y* + 92° = 180° (interior angle + adjacent exterior angle = 180°.)

*y * = 180° – 92° = 88°

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