The measure of one angle is 7 times the measure of its complement. Find the measure of each angle.
x = 7(90 - x)
x = 630 - 7x
8x = 630
x = 78.75
90 - 78.75 = 11.25
so the measures are 78.75 degrees and 11.25 degrees.
Well, if you have an angle and you're looking for its complement, you must not be feeling very complete. Just remember the saying, "Complements complete you!" It's like finding your missing puzzle piece.
Now, let's say the smaller angle is x degrees. The complement of the smaller angle would then be 90 - x degrees. According to the problem, the larger angle is 7 times the measure of its complement. So, the larger angle would be 7(90 - x) degrees.
Now we have two equations:
1. x = smaller angle
2. 7(90 - x) = larger angle
Let's solve this puzzle:
Start with equation 2:
7(90 - x) = 7(90) - 7x
630 - 7x = 630 - 7x
Whoops! Looks like we've reached a dead end. This puzzle must have all the pieces in place. The only solution is that the smaller angle is 0 degrees and the larger angle is its complement, 90 degrees.
Sorry, it seems like this angle problem is no laughing matter!
Let's represent the measure of one angle as x.
The measure of its complement would be 90 - x (since the sum of angles in a right angle is 90 degrees).
Given that one angle is 7 times the measure of its complement, we can write the equation:
x = 7(90 - x)
Now, let's solve for x.
Expanding the equation:
x = 630 - 7x
Combining like terms:
x + 7x = 630
8x = 630
Dividing both sides by 8:
x = 78.75
So, one angle measures 78.75 degrees.
To find the measure of its complement, we substitute x back into the equation:
90 - x = 90 - 78.75 = 11.25
Therefore, the measure of each angle is 78.75 degrees and 11.25 degrees.
To solve this problem, we need to understand what complementary angles are. Complementary angles add up to 90 degrees. Let's call one angle x, and its complement (the angle that adds up to 90 degrees with x) y.
Based on the given information, we know that x is 7 times the measure of its complement, so we can write the equation:
x = 7y
We also know that the sum of these angles is 90 degrees:
x + y = 90
Now we can solve these equations simultaneously to find the values of x and y.
First, substitute the value of x from the first equation into the second equation:
7y + y = 90
8y = 90
y = 90/8
y = 11.25
Now substitute the value of y back into the first equation to find x:
x = 7(11.25)
x = 78.75
So, the measure of the first angle is 78.75 degrees, and the measure of its complement is 11.25 degrees.