If l||m and l∠6 = 4x - 15 and m∠7 = x + 30, then l∠6 =?

Solution:

The information provided in the problem statement can be depicted in the diagram below. Also given is the angle

The lines l and m are parallel and make the angles l∠6 = 4x - 15 and m∠7 = x + 30 with the horizontal as shown above.

From the property of parallel lines it can be inferred that: these are the corresponding angles.

l∠6 = m∠7

4x - 15 = x + 30

3x = 45

x = 15

Therefore

l∠6 = 4x -15

= 4 × 15 - 15

= 60 - 15 = 45°.

If l||m and l∠6 = 4x - 15 and m∠7 = x + 30, then l∠6 =?

Summary:

Given l||m and l∠6 = 4x - 15 and m∠7 = x + 30, then l∠6 = 45°.