Question

Lines a and b are parallel in the diagram what is the measure of angle 1

Answer 1

45

Explanation:

Upon examining the graph, you can realize that angle 3x is the same as the angle directly to the left of 9x. Since that makes a straight line, we can realize that that sums up to 180. We call this a linear pair.

so you have:

3x+9x = 12x = 180

x = 15

A important concept to know here is vertical angles. Vertical angles occur when two lines intersect each other. The opposite angles formed at an intersection are congruent, which is why 1 is congruent to 3x.

Therefore, angle 1 is 45 degrees.