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? and the samller
Two complementary angle sum up to give 90 degrees.
Angle 1 = x
Angle 2 = (5/8)x
x + (5/8)x = 90
Solve for x
x + 5 x/8 = 90
8 x + 5 x = 720
13 x = 720
x = 55.38
5x/8 = 34.62
thx
To find the measure of the larger angle, we can assign variables to both angles and set up an equation based on the given information.
Let's say the measure of one angle is x degrees. Since the measure of one angle is 5/8 the measure of the other, we can represent the other angle as (5/8)x degrees.
Since the two angles are complementary, their measures add up to 90 degrees. So, we can set up the equation:
x + (5/8)x = 90
To solve this equation, we need to combine like terms:
(8/8)x + (5/8)x = 90
(13/8)x = 90
Now, we can solve for x by multiplying both sides of the equation by the reciprocal of (13/8), which is (8/13):
(8/13) * (13/8)x = (8/13) * 90
x = 720/13
Thus, the measure of the smaller angle is 720/13 degrees.
To find the measure of the larger angle, we can substitute the value we found for x:
(5/8) * (720/13) = 3600/104
Thus, the measure of the larger angle is 3600/104 degrees, which can be simplified to 75/13 degrees.