Lines b and c are parallel. What is the measure of 6?
a) m6 = 45°
b) m6 = 54°
c) m6 = 117°
d) m6 = 126°
Parallel lines never cut (intersect) or meet each other, and they lie on the same plane.
Answer: The measure of angle 6 for the given diagram is option (b) m6 = 54°.
Let's look into the steps below
Explanation:
As you see in the given figure, we have that:
⇒ m∠6 = m∠2 (corresponding angles) ----------- (1)
⇒ m∠6 = (5x + 9)º (vertical angles)
So,
⇒ m∠2 = (5x + 9)º [From (1)] --------------- (2)
Alos, (13x + 9)º + m∠2 = 180º (Linear pair) ------------------ (3)
Substitute (2) in equation (3)
⇒ (13x + 9)º + (5x +9)º = 180º
⇒ (18x + 18)º = 180º
⇒ 18x = 180º - 18º
⇒ x = 9º
Now, we know that
m∠6 = (5x + 9)º
Put the value of x to find m∠6
⇒ m∠6 = (5 × 9 + 9)º
⇒ m∠6 = 54º