Question

which of the following statements must be true about this diagram? check all that apply. a. the degree measure of ∠4 equals the sum of the degree measures of ∠2 and ∠3. b. m∠3 is greater than m∠2 c. m∠4 is greater than m∠2. d. the degree measure of ∠4 equals the sum of the degree measures of ∠1 and ∠2. e. m∠4 is greater than m∠1. f. the degree measure of ∠3 equals the sum of the degree measures of ∠1 and ∠2

Explanation:

Step1: Recall exterior - angle theorem

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. The non - adjacent interior angles to $\angle4$ are $\angle1$ and $\angle2$. So, $m\angle4=m\angle1 + m\angle2$.

Step2: Analyze angle - size relationships

Since $m\angle4=m\angle1 + m\angle2$, then $m\angle4>m\angle1$ and $m\angle4>m\angle2$.

Answer:

D. The degree measure of $\angle4$ equals the sum of the degree measures of $\angle1$ and $\angle2$;
E. $m\angle4$ is greater than $m\angle1$;
C. $m\angle4$ is greater than $m\angle2$