Question

show that the measure of an exterior angle is always equal to the sum of the measures of its non - adjacent interior angles. use the figure below to help.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In triangle with angles 1, 2, 3, we have $\angle1+\angle2+\angle3 = 180^{\circ}$.

Step2: Consider the linear - pair property

$\angle3$ and $\angle4$ form a linear - pair. So, $\angle3+\angle4=180^{\circ}$.

Step3: Equate the two expressions

Since $\angle1+\angle2+\angle3 = 180^{\circ}$ and $\angle3+\angle4 = 180^{\circ}$, we can set them equal to each other: $\angle1+\angle2+\angle3=\angle3+\angle4$.

Step4: Solve for $\angle4$

Subtract $\angle3$ from both sides of the equation $\angle1+\angle2+\angle3=\angle3+\angle4$. We get $\angle4=\angle1+\angle2$.

Answer:

We have shown that the measure of an exterior angle ($\angle4$) is equal to the sum of the measures of its non - adjacent interior angles ($\angle1$ and $\angle2$).