# Exterior Angle Theorem

For a triangle:

- The exterior angle
**d**equals the angles**a plus b**. - The exterior angle
**d**is greater than angle**a**, or angle**b**.

### Example:

The exterior angle is **35° + 62° = 97°**

And **97°** > **35°**

And **97°** > **62°**

## Why?

Because the interior angles of a triangle add to 180°, and angles c+d also add to 180°:

The interior angles of a triangle add to 180°:a + b + c = 180°

Angles

**c**and**d**make a straight angle, which is 180°:d + c = 180°So

**d + c**equals**a + b + c**:d + c = a + b + cSubtract

**c**from both sides:d = a + b## Works For Any Triangle's Exterior Angle

### Example:

The exterior angle is **40° + 27° = 67°**

And **67°** > **40°**

And **67°** > **27°**

### Example: How big is angle **d**?

We can't calculate exactly, but we **can** say:

**d°** > **61°**