If the measures of one of the angles in a complementary pair is 20˚ more than that of the other find the measure of each angle
smaller angle --- x
larger angle -----x+20
complementary angles add up to 90°
so ....
To find the measure of each angle in a complementary pair, let's start by assigning variables to the angles. Let's call one angle x and the other angle y.
Now, we know that the measures of the angles in a complementary pair add up to 90 degrees. So, we can write the equation:
x + y = 90
We are also given that one of the angles is 20 degrees more than the other. This can be expressed as an equation:
x = y + 20
Now, we have a system of two equations:
x + y = 90
x = y + 20
To solve this system of equations, we can substitute the value of x from the second equation into the first equation:
(y + 20) + y = 90
Simplifying the equation, we get:
2y + 20 = 90
Next, let's isolate the variable y by subtracting 20 from both sides:
2y = 70
Finally, dividing both sides by 2, we find:
y = 35
Now that we have the value of y, we can substitute it back into one of the original equations to solve for x:
x = y + 20
x = 35 + 20
x = 55
Therefore, the measure of each angle is 35 degrees and 55 degrees.