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. first identify the types of angles in the figure. the exterior angle is ∠4. the non - adjacent interior angles are ∠1 and ∠2. what is the relationship between angles 3 and 4? m∠3 + m∠4 = 180 what is the relationship between the interior angles? m∠1 + m∠2 + m∠3 =

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180 degrees. So, for the given triangle with interior angles $\angle1$, $\angle2$, and $\angle3$, we have $m\angle1 + m\angle2 + m\angle3=180$.

Step2: Recall linear - pair property

Angles $\angle3$ and $\angle4$ form a linear - pair. By the linear - pair postulate, $m\angle3 + m\angle4 = 180$.

Step3: Equate the two expressions

Since $m\angle1 + m\angle2 + m\angle3=180$ and $m\angle3 + m\angle4 = 180$, we can set $m\angle1 + m\angle2 + m\angle3=m\angle3 + m\angle4$.

Step4: Solve for $m\angle4$

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

Answer:

180