measure of angle A and measure of angle B are complementary. measure of angle A = 3x + 12 and measure of angle B = 2x - 22.
Find the measure of each angle.
Given that angles A and B are complementary, we know that their measures add up to 90 degrees.
So, we can set up an equation:
(3x + 12) + (2x - 22) = 90
Now, let's solve for x.
Combining like terms, we have:
5x - 10 = 90
Adding 10 to both sides of the equation:
5x = 100
Dividing both sides by 5, we get:
x = 20
Now, let's find the measure of angle A and angle B using the value of x.
Angle A = 3x + 12
Angle A = 3(20) + 12
Angle A = 60 + 12
Angle A = 72
Angle B = 2x - 22
Angle B = 2(20) - 22
Angle B = 40 - 22
Angle B = 18
Therefore, the measure of angle A is 72 degrees and the measure of angle B is 18 degrees.
To find the measure of each angle, we first need to understand that complementary angles add up to 90 degrees. So, we can set up an equation and solve for x.
The measure of angle A is given as 3x + 12, and the measure of angle B is given as 2x - 22. Since they are complementary, we can write the equation:
(3x + 12) + (2x - 22) = 90
Now, let's solve this equation for x:
Combine like terms:
3x + 2x + 12 - 22 = 90
5x - 10 = 90
Add 10 to both sides of the equation:
5x - 10 + 10 = 90 + 10
5x = 100
Divide both sides of the equation by 5:
5x/5 = 100/5
x = 20
Now that we know the value of x is 20, we can substitute it back into the expressions for the angles to find their measures:
Measure of angle A = 3x + 12
Measure of angle A = 3(20) + 12
Measure of angle A = 60 + 12
Measure of angle A = 72 degrees
Measure of angle B = 2x - 22
Measure of angle B = 2(20) - 22
Measure of angle B = 40 - 22
Measure of angle B = 18 degrees
Therefore, the measure of angle A is 72 degrees and the measure of angle B is 18 degrees.
3x + 12 + 2x - 22 = 90
5x - 10 = 90
5x = 100
x = _______ degrees