Answer:
Step-by-step explanation:
5). ∠2 ≅ ∠6
By corresponding angles theorem both the angles will be congruent.
6). m∠3 + m∠5 = 180°
If two lines are parallel and a transverse cut these parallel lines, pair of consecutive angles in one side of the transverse are supplementary.
[Consecutive interior angles theorem]
7). Given : m∠1 = 71°
Therefore, m∠1 = m∠5 = 71°
By corresponding angles theorem ∠1 and ∠5 are corresponding angles.
The classification of each pair of angles and their measures as well as the postulate or theorem that justifies it have been detailed below.
5) From the given image, we see that;
Two parallel lines are cut by a transversal, then from corresponding angles theorem we can say that the pairs of corresponding angles are congruent. ∠2 and ∠6 are congruent.
Thus;
∠2 ≅ ∠6
6) We see that m∠3 and m∠5 are a pair of consecutive angles on one side of the transverse line.
Thus, we can say from Consecutive interior angles theorem that m∠3 and m∠5 are supplementary. This means they sum up to 180°. Thus;
m∠3 + m∠5 = 180°
7) We are told that m∠1 = 71°
From corresponding angles definition as defined earlier, we can say that; m∠1 = m∠5 are corresponding angles and as such they are congruent. Thus;
m∠1 = m∠5 = 71°
Thus; m∠5 = 71°
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