Question

Which of the following pairs of angles is not necessarily congruent

Answer 1

Answer:

E. $\angle 3$ and $\angle 5$.

Explanation:

According to the figure, we have the following conclusions:

1) $\angle 1$ and $\angle 2$ are vertical opposite angles. ($m \angle 1 = m \angle 2$)

2) $\angle 2$ and $\angle 3$ are internal alternate angles. ($m \angle 2 = m\angle 3$)

3) $\angle 2$ and $\angle 4$ are corresponding angles. ($m\angle 2 = m\angle 4$)

4) $\angle 3$ and $\angle 4$ are vertical opposite angles. ($m \angle 3 = m \angle 4$)

But, $\angle 3$ and $\angle 5$, since $m \angle 3 + m\angle 6 + m\angle 5 = 180^{\circ}$, where $\angle 3$ is an acute angle and $\angle 6$ is a right angle, and $m \angle 4 + m \angle 5 = 90^{\circ}$. Then,

$m\angle 5 = 90^{\circ} -m\angle 4$.

$m\angle 5 = 90^{\circ}-m\angle 3$

Hence, the right answer is E.