Answer: See Below
Explanation:
Concept:
Here, we need to know the idea of alternative interior angle, alternative exterior angle, and corresponding angles.
Alternative interior angle: a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.
Alternative exterior angle: a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.
Corresponding angle: A pair of angles that occupy the same relative position at each intersection where a straight line crosses two others.
All three kinds of angles above occur to be congruent (equal) when the lines are parallel to each other.
If you are still confused, please refer to the attachment below for a graphical explanation
Solve:
PART ONE
a) Name two pairs of alternative exterior angles: ∠1 and ∠7 / ∠2 and ∠8
b) Name two pairs of corresponding angles: ∠1 and ∠5 / ∠2 and ∠6
c) Name two pairs of alternative interior angles: ∠4 and ∠6 / ∠3 and ∠5
PART TWO
a) If the measure of angle 7 is 52°, what is the measure of angle 1?
- As we can see from above, ∠1 and ∠7 are alternative exterior angles.
- They are part of parallel lines, thus according to the properties, they are equal.
- m∠1 = m∠7 = 52°
b) If the measure of angle 8 is 112°, then what is the measure of angle 3?
- As we can see from the figure given, ∠8 and ∠7 are linear pairs or supplementary angles, which adds up to 180°.
- m∠7 = 180 - m∠8 = 180 - 112 = 68°
- As we can see from the figure given, ∠7 and ∠3 are corresponding angles.
- They are part of parallel lines, thus according to the properties, they are equal.
- m∠3 = m∠7 = 68°
Hope this helps!! :)
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