Question

For the following figure, complete the statement about the diagram. Then state the definition, postulate or theorem that justify the answer. $m\angle 1+m\angle 4=\_\_$

Short answer

The statement is$m\angle 1+m\angle 4={180}^{\circ }$.

Step-by-step solution

Step 1- Check the figure.

Consider the figure.

Step 2- Apply the concept of the supplementary angles.

Linear pair or supplementary angles states that the sum of angles 1 and 4 must be 180 degree.

Step 3- Step description.

Since the sum of the supplementary angles is 180 degrees thus the sum of the angles 1 and 4 will be 180 degrees.

Thus, the statement is$m\angle 1+m\angle 4={180}^{\circ }$ and the postulate is addition postulate.