FIND THE MEASURES OF ANGLE 1 AND ANGLE 2 IF MEASURE ANGLE 1=3X-12 MEASURE ANGLE 2=7X+2 AND ANGLE 1 AND ANGLE 2 FORM A LINEAR PAIR

To find the measures of angle 1 and angle 2, we need to remember that when two angles form a linear pair, they add up to 180 degrees.

So, we can set up an equation using the given measures:

(Measure of Angle 1) + (Measure of Angle 2) = 180

Substituting the given expressions for the measures of angle 1 and angle 2, we have:

(3x - 12) + (7x + 2) = 180

Now, let's solve the equation for x:

Combine like terms: 3x + 7x - 12 + 2 = 180

Simplify: 10x - 10 = 180

Add 10 to both sides of the equation: 10x - 10 + 10 = 180 + 10

Simplify: 10x = 190

Now, divide both sides of the equation by 10: 10x/10 = 190/10

Simplify: x = 19

Now that we have found the value of x, we can substitute it back into the expressions for the measures of angle 1 and angle 2:

Measure of Angle 1 = 3x - 12 = (3 * 19) - 12 = 57 - 12 = 45 degrees

Measure of Angle 2 = 7x + 2 = (7 * 19) + 2 = 133 + 2 = 135 degrees

Therefore, the measure of Angle 1 is 45 degrees, and the measure of Angle 2 is 135 degrees.

linear pair means the sum of the angles equal 180 degrees. therefore,

3x - 12 + 7x + 2 = 180
10x - 10 = 180
10x = 190
x = 19
finally, substituting this back to angle 1 and 2:
Angle 1: 3(19) - 12 = 45 degrees
Angle 2: 7(19) + 2 = 135 degrees

hope this helps~ :)