Answer:
Please check the explanation.
Step-by-step explanation:
From the given diagram, we can observe that r and s are the two parallel lines intersected by the two transversal lines.
Therefore, the pairs of alternating interior angles formed by the two transversal lines are:
We know that alternating interior angles formed by a transversal line are congruent.
Thus,
Part a)
Given
m∠1 = 3x + 42
m∠5 = 8x - 8
As
∠1 = ∠5
So
3x + 42 = 8x - 8
flipe the equation
8x - 8 = 3x + 42
subtract 3x from both sides
8x - 8 - 3x = 3x + 42 - 3x
5x - 8 = 42
add 8 to both sides
5x - 8 + 8 = 42 + 8
5x = 50
divide both sides by 5
5x/5 = 50/5
x = 10.0000 (Rounded to four decimal places)
Thus, the value of x = 10.0000 (Rounded to four decimal places)
Part b)
Given
m∠6 = 12°
It is clear that angles ∠6 and angle ∠7 lie on a straight line.
Thus,
The sum of ∠6 and ∠7 is 180°.
∠6 + ∠7 = 180°
substituting m ∠ 6 = 12° in ∠6 + ∠7 = 180°
12° + ∠7 = 180°
subtract 12 from both sides
12° + ∠7 - 12° = 180° - 12°
∠7 = 168°
Thus, measure of angle ∠7 = 168°.
We already know that alternating interior angles formed by a transversal line are congruent.
∠7 and ∠2 are alternating interior angles.
Thus,
∠2 = ∠7
As ∠7 = 168°.
Therefore,
∠2 = 168°
Hence, we conclude that
∠2 = 168°
