Question

Lines m and n are parallel, as shown in the diagram below. What are the measures of angles A and B? Hint: The sum of all interior angles of a triangle must equal 180 degrees.

Answer 1

`\boxed{A = 55\°}`

`\boxed{B = 60\°}`

Explanation:

Exterior Angle with A = 180 - 55 = 125 degrees (Angles on a straight line)

The measure of exterior angle is equal to the sum of non-adjacent interior angles.

So,

125° = B + 65°

B = 125 - 65

B = 60°

Now,

A = 180 - 60 - 65 (Interior angles of a triangle add up to 180 degrees)

A = 55°

Answer 2

A = 55

B = 60

Explanation:

We know that 55+ b+ other angle = 180 since they make a straight line

The other angle = 65 since they are alternate interior angles

55+ B+ 65 = 180

Combine like terms

120 + B = 180

B = 60

A + B + 65 = 180 interior angles of a triangle must equal 180 degrees

A +60+ 65 =180

Combine like terms

A +125 = 180

A = 55