# How is the triangle exterior angle theorem related to the triangle angle sum theorem?

**exterior angle theorem**states that the

**exterior angle**formed when you extend the side of a

**triangle**is equal to the

**sum**of its non-adjacent

**angles**. The

**theorem**tells us that the measure of

**angle**D is equal to the

**sum**of

**angles**A and B.

Keeping this in view, what is the triangle exterior angle theorem?

The **exterior angle theorem** is Proposition 1.16 in Euclid's Elements, which states that the measure of an **exterior angle** of a **triangle** is greater than either of the measures of the remote interior **angles**. This is a fundamental result in absolute geometry because its proof does not depend upon the parallel postulate.

**theorem**. If the equivalent angle is taken at each

**vertex**, the exterior angles always add to 360° In fact, this is true for any convex

**polygon**, not just triangles.

Just so, what is the relationship between exterior and interior angle of a triangle?

The **angles** on the inside are called **Interior angles**. The sum of the **interior angles of a triangle** is always 180 degrees. The **exterior angle** is the **angle between** any side of a shape, and a line extended from the next side. The sum of an **exterior angle** and its adjacent **interior angle** is also 180 degrees.

Definition & Formula. The exterior angle theorem states that the exterior angle formed when you extend the side of a **triangle** is equal to the **sum** of its non-adjacent angles. Remember, our non-adjacent angles are those that don't touch the angle we are working with.