Question

select all the true statements given the figure. a. m∠4 = m∠2 b. m∠4 = m∠1 + m∠2 c. m∠4 = 180 - m∠3 d. m∠4 = m∠1 + m∠2 + m∠3 e. m∠4 = m∠3 + m∠1

Explanation:

Step1: Recall exterior - angle property

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. In the given triangle, $\angle4$ is an exterior angle and $\angle1$ and $\angle2$ are the non - adjacent interior angles. So, $m\angle4=m\angle1 + m\angle2$.

Step2: Recall linear - pair property

$\angle3$ and $\angle4$ form a linear pair. Since the sum of the measures of angles in a linear pair is $180^{\circ}$, we have $m\angle4=180 - m\angle3$.

Answer:

B. $m\angle4 = m\angle1 + m\angle2$
C. $m\angle4 = 180 - m\angle3$