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bezimeni [28]3 years ago

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Which of the following pairs of angles is not necessarily congruent

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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.

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