Recall that two angles are complementary if the sum of their measures is 90°. Find the measures of two complementary angles if one angle is five times the other angle.
5a+a=90
6a=90
a=15
larger angle=75
75+15=90
smaller angle would be 15 and larger angle would be 75
5a+a=90
6a=90
a=15
To find the measures of two complementary angles, we need to set up an equation using the given information.
Let's assume that one angle is represented by x. Since the other angle is five times the first angle, we can represent it as 5x.
According to the definition of complementary angles, their sum is 90°. Therefore, we have the equation:
x + 5x = 90
Combining like terms:
6x = 90
To solve for x, we divide both sides of the equation by 6:
x = 90/6
Simplifying:
x = 15
So one angle is 15°. To find the other angle, we substitute this value back into our equation:
5x = 5 * 15
5x = 75
Therefore, the other angle is 75°.
Hence, the measures of the two complementary angles are 15° and 75°.
5a + a = 90
6a = 90
a = ?