Question

For the following figure, complete the statement about the diagram. Then state the definition, postulate or theorem that justify the answer.$m\angle 1+m\angle 2+m\angle 3=\_\_$

Short answer

The statement is$m\angle 1+m\angle 2+m\angle 3={180}^{\circ }$.

Step-by-step solution

Step 1- Check the figure.

Consider the figure.

Step 2- Apply the concept of the angle sum theorem of the triangle.

Angel sum theorem of a triangle states that the sum of the measure of interior angles of a triangle is 180 degrees.

Step 3- Step description.

Since the sum of the measure of the interior angles of a triangle is 180 degrees thus the sum of the angles 1,2 and 3 will be 180 degrees.

Thus the statement is $m\angle 1+m\angle 2+m\angle 3={180}^{\circ }$ and the theorem is angle sum theorem.