Geometry angles

Question

The measure of angle 2 is twelve less than five times the measure of angle 1. If angle 1 and angle 2 form a linear pair, find the measure of angle 2.

Answer 1

A linear pair of angles has a sum of 180 degrees (by definition). Write an algebraic equation given the other information you have:

Let the measure of Angle 2 = x

Let the measure of Angle 1 = y

By the definition above,

(equation 1) x + y = 180

from the rest of the given information,

(equation 2) x = 5y-12 (M2 is 12 less than 5 times M1)

Now solve using the usual techniques for a system of equations. For instance:

Solve eq 1 for x:

x = 180 - y

Substitute this new expression for x into eq 2"

180 - y = 5y - 12

180 = 6y - 12 (adding y to both sides)

192 = 6y (adding 12 to both sides

ANS 1 --> 32 = y (dividing both sides by 6)

Now plug the value of y into the first equation:

x + y = 180

x + 32 = 180 (substitution)

ANS 2---> x = 148 (subtracting 32 from both sides)