Find the measure of two complementary angles if the measure of one angle is 5/8 the measure of the other. What is the measure of the larger angle?
90 / 8 = 11.25
11.25 * 5 = ?
large angle --- x
smaller angle = 5x/8
x + 5x/8 = 90
8x + 5x = 720
13x = 720
x = 720/13 = appr 55.38°<----- the larger
the smaller is 34.62°
check: 34.62 + 55.38 = 90
(5/8)(55.38) = appr 34.61 , off because of rounding error
To find the measure of two complementary angles, we first need to understand what complementary angles are. Complementary angles are two angles whose sum is 90 degrees.
Let's assume that one angle is x degrees. According to the problem, the measure of one angle is 5/8 the measure of the other. So, the other angle would be (5/8) * x degrees.
The sum of the two angles is 90 degrees, as they are complementary. So, we can set up an equation:
x + (5/8) * x = 90
To solve for x, we can simplify the equation:
(8/8) * x + (5/8) * x = 90
(13/8) * x = 90
To isolate x, we can multiply both sides of the equation by the reciprocal of (13/8), which is (8/13).
x = (90 * 8) / 13
x ≈ 55.38 degrees
So, one angle is approximately 55.38 degrees. To find the measure of the larger angle, we can substitute this value back into the equation:
(5/8) * x = (5/8) * 55.38 ≈ 34.61 degrees
Therefore, the measure of the larger angle is approximately 34.61 degrees.