Question

State if the following statement is true or false:

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

• A. True
• B. False
• C. Aambiguous
• D. Data Insufficient

Answer 1

The correct option is A True

Let's try and prove the exterior angle property for a triangle.

For the given triangle $XZY$,

$\angle 1+\angle 2+\angle XZY={180}^o$

Also, $\angle 3+\angle XZY={180}^o$ ......... (Linear pair of angles)

$\angle 1+\angle 2+\angle XZY=\angle 3+\angle XZY$

$\Rightarrow \angle 3=\angle 1+\angle 2$ ...... (which is the Exterior angle property).

Therefore, we can say that an exterior angle of a triangle is equal to the sum of the two interior opposite angles.
That is, the statement is true.

Hence, option $A$ is correct.