Two complementary angles are such that one is eight times larger than the other. Find the two angles.
let x = first angle
let 90-x = second angle
then we set up the equation:
8x = (90-x)
8x + x = 90
9x = 90
x = 10 degrees
90-x = 80 degrees
hope this helps~ :)
To find the two complementary angles, we need to first understand what complementary angles are.
Complementary angles are two angles whose measures add up to 90 degrees. In other words, if you add the measure of one angle to the measure of its complement, the result will be 90 degrees.
Let's say the measure of one angle is x degrees. According to the problem statement, the other angle is eight times larger than the first angle. Therefore, the measure of the second angle would be 8x degrees.
Using the definition of complementary angles, we can set up the following equation:
x + 8x = 90
Combining like terms:
9x = 90
Dividing both sides by 9:
x = 10
So, the measure of one angle is 10 degrees, and the measure of the other angle is 8 times larger, which is 8 * 10 = 80 degrees.
Therefore, the two angles are 10 degrees and 80 degrees.
Let's say one angle is x degrees.
According to the problem, the other angle is eight times larger than the first angle. Therefore, the second angle is 8x degrees.
Since two angles are complementary, their sum is 90 degrees.
So, we can set up the equation: x + 8x = 90
Combining like terms, we have: 9x = 90
Dividing both sides by 9, we get: x = 10
Therefore, the first angle is 10 degrees and the second angle is 8 times larger, which is 8 * 10 = 80 degrees.