Find the measure of two complementary angles if the measure of one angle is 30˚ greater than the measure of the other. What is the measure of the larger angle?
What is the measure of the smaller angle?
A=30+B
A+B=90
30+B+B=90
B=30
A=60
To find the measure of the larger angle, we can set up an equation based on the information given.
Let x be the measure of the smaller angle.
According to the problem, the measure of the larger angle is 30˚ greater than the measure of the smaller angle, so the measure of the larger angle is x + 30˚.
Since two angles are complementary, their sum is 90˚.
Therefore, we can set up the following equation:
x + (x + 30˚) = 90˚
Simplifying the equation:
2x + 30˚ = 90˚
Subtracting 30˚ from both sides:
2x = 60˚
Dividing both sides by 2:
x = 30˚
So, the measure of the smaller angle is 30˚.
To find the measure of the larger angle, we substitute the value of x (which is 30˚) into the equation:
x + 30˚ = 30˚ + 30˚ = 60˚
Therefore, the measure of the larger angle is 60˚.