Question

For the following figure, complete the statement about the diagram. Then state the definition, postulate or theorem that justify the answer. $m\angle 1+m\angle 2=m\angle \_\_$

Short answer

The statement is$m\angle 1+m\angle 2=m\angle 5$.

Step-by-step solution

Step 1- Check the figure.

Consider the figure.

Step 2- Apply the concept of the exterior angle property.

In a triangle, the exterior angle is always equal to the sum of the interior opposite angle. This property is known as exterior angle property. Any two triangles will be similar if their corresponding angles tend to be congruent and length of their sides will be proportional.

Step 3- Step description.

Sinceexterior angle of triangle is sum of opposite interior angles thus the sum of angle 1 and 2 will be equal to angle 5.

Thus, the statement is$m\angle 1+m\angle 2=m\angle 5$ and the postulate is exterior angle property.