Suppose that angle MAP and angle MAC are linear pairs angle MAP=7x-13 and angle MAC=3x+13. Identify the line and the rays that form angle MAP and angle MAC.

Answer 1

Can't see the figure in your problem, but it seems like it's the following:

M

/

7x-13 / 3x+13

P-------------A---------------------C

Since ∠ MAP and ∠MAC form a linear pair, the sum to 180^o. So:

m∠MAP + m∠MAC = 180

7x-13 + 3x+13 = 180

Solve for x then solve for m∠MAP and m∠MAC.

Answer 2

An angle is named by naming a point on one ray, the vertex, and a point on the second ray. Thus the linear pair is on line PC. A is somewhere between P and C on the line. M is a point above the line with AM ray going from the line to M. The angle MAP contains rays AM and AP. The angle MAC contains rays AM and AC.

A line has 180 degrees between its ends. Thus the sum of the degrees of the two angles is 180. Angle MAP + Angle MAC = 180. By substitution 7x-13 + 3x+13 = 180.

Combine terms to have 10x = 180. Thus x is 18.

The measure of angle MAP is 7(18) -13 or 113 degrees and the measure of angle MAC is 3(18) + 13 or 67 degrees.