Question

2 tries left. please try again. select the angle(s) with measures that are greater than m∠2. triangle and angle diagram a) ∠5 b) ∠6 c) ∠4 d) ∠7 e) ∠3 f) ∠1

Explanation:

Step1: Use exterior angle theorem

For $\triangle TUV$, $\angle 4$ is an exterior angle, so $m\angle 4 = m\angle 2 + m\angle 3$, thus $m\angle 4 > m\angle 2$.

Step2: Use exterior angle theorem

For $\triangle TUW$, $\angle 7$ is an exterior angle, so $m\angle 7 = m\angle 1 + m\angle 3 + m\angle 2$, thus $m\angle 7 > m\angle 2$.

Step3: Use exterior angle theorem

For $\triangle TUW$, $\angle 1$ is an exterior angle, so $m\angle 1 = m\angle 2 + m\angle 3$, thus $m\angle 1 > m\angle 2$.

Step4: Compare angles in $\triangle UWV$

In $\triangle UWV$, $\angle 5 + m\angle 6 + m\angle 4 = 180^\circ$, and $m\angle 2 + m\angle 3 + m\angle 1 = 180^\circ$. Since $m\angle 1 > m\angle 2$, $m\angle 5$ and $m\angle 6$ cannot be confirmed greater than $m\angle 2$. $m\angle 3$ is part of the sum with $m\angle 2$, so $m\angle 3 < m\angle 2$.

Answer:

C) $\angle 4$, D) $\angle 7$, F) $\angle 1$