Answer:
m∠3 = 60°
m∠6 = 60°
Step-by-step explanation:
If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent. This is called the "Alternate Interior Angles Theorem".
As line p intersects the set of parallel lines m and n at two distinct points, then m∠3 = m∠6 and m∠4 = m∠5
Given:
- m∠3 = (7x - 10)°
- m∠6 = (5x + 10)°
As m∠3 = m∠6, then:
⇒ 7x - 10 = 5x + 10
Add 10 to both sides:
⇒ 7x - 10 + 10 = 5x + 10 + 10
⇒ 7x = 5x + 20
Subtract 5x from both sides:
⇒ 7x - 5x = 5x + 20 - 5x
⇒ 2x = 20
Divide both sides by 2:
⇒ 2x ÷ 2 = 20 ÷ 2
⇒ x = 10
Now substitute the found value of x into one of the angle expressions:
m∠3 = 7(10) - 10
= 70 - 10
= 60°
As m∠3 = m∠6, then m∠6 = 60°
