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?
x + (x-30) = 90
2 x = 120
#1 = X Deg.
#2 = x+30o.
x + (x+30) = 90.
To find the measure of the larger angle, we need to first set up an equation based on the given information.
Let's assume that the measure of one angle is x degrees.
According to the given information, the measure of the other angle is 30˚ greater than x. Therefore, the measure of the second angle can be represented as (x + 30˚).
Complementary angles are two angles that add up to 90˚. So, we can set up the equation:
x + (x + 30˚) = 90˚
Now, let's solve the equation to find the value of x.
2x + 30˚ = 90˚ (combine like terms)
2x = 90˚ - 30˚ (subtract 30˚ from both sides)
2x = 60˚
Finally, divide both sides of the equation by 2:
x = 60˚ / 2
x = 30˚
Therefore, the measure of the larger angle is (x + 30˚) which is (30˚ + 30˚) = 60˚.