Two angles are complementary.The sum of the first angle and half the second angle is 82 degrees. Find the measures of the angles.
What is the measure of the smaller angle?
What is the measure of the other angle?
complentary angles add up to 90
so if one angle is x, the other must be 90-x
so (90-x) + (1/2)x = 90
should be easy to solve for x
To solve this problem, let's start by assigning variables to the measures of the angles. Let's call the first angle x and the second angle y.
We are given that the angles are complementary, which means that their sum is equal to 90 degrees. So we can write the equation:
x + y = 90 (Equation 1)
Next, we are given that the sum of the first angle and half the second angle is equal to 82 degrees. So we can write another equation:
x + (1/2)y = 82 (Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) with two variables (x and y). We can solve this system to find the values of x and y.
One way to solve this system is by substitution. Let's solve Equation 1 for x:
x = 90 - y
Now we can substitute this expression for x in Equation 2:
(90 - y) + (1/2)y = 82
Simplifying the equation:
90 - y + (1/2)y = 82
90 - y/2 + y/2 = 82
90 = 82
This implies that there is no possible value of y that satisfies this equation. Thus, there is no solution to this problem.
Therefore, the problem cannot be solved, and we cannot determine the measure of the smaller angle or the measure of the other angle.