Question

HELP ME ! Lines l and m are parallel.

Parallel lines l and m are cut by transversals s and t. Clockwise from top left, the angles formed by s, t, and l are blank, 85 degrees, (2 x) degrees, (x minus 10) degrees, 1, blank; formed by s and m are blank, 2, blank, blank; formed by t and m are 3, blank, blank, blank.

What is the measure of angle 3?
25 degrees
35 degrees
70 degrees
85 degrees

Answer 1

The correct option is A

A) 25 degrees

Explanation:

As two parallel line l and m are cut by the line t, the angles formed (x-10)° and < 3 are alternate angles, therefore they are equal to each other.

< 3 = (x-10)° ⇒ Equation (i)

We know that any straight line has a sum of angles equal to 180°.

Consider line t, it is divided into 3 angles due to cutting. Those angles are 85°, (2x)° and (x-10)°. The sum of these angles is 180° as stated before.

85° + (2x)° + (x-10)° = 180°

Find the value of x:

85 +2x + x - 10 = 180

3x + 75 = 180

3x = 105

x = 35°

Substitute it in Equation (i) to get the value of <3

< 3 = (35 - x)°

< 3 = (35 - 10)°

< 3 = 25°