Help please :)
The measure of the supplement of an angle is 20 degrees more than three times the measure of the original angle. Find the measures of the angles.
The measures of an angle and its complement differ by 22 degrees. Find the measures of the angles.
1) 180 - A = 3A + 20
4A = 160
A = 40 degrees is the angle
2) 90 - A - A = 22
2A = 68
A = 34 degrees. The other angle (the complement) is 90 - 34 = 56 degrees
Even if you haven't studied algebra yet, I hope you can follow the logic
To solve these types of problems, we can set up equations based on the given information and use algebra to find the measures of the angles. Let's solve the problems step by step.
Problem 1: The measure of the supplement of an angle is 20 degrees more than three times the measure of the original angle. Find the measures of the angles.
Let's assume the original angle's measure is x degrees.
According to the problem, the supplement of the angle (180 - x degrees) is 20 degrees more than three times the measure of the original angle (3x + 20 degrees).
So, we can write the equation:
180 - x = 3x + 20
Now, let's solve the equation to find the value of x:
180 - 20 = 3x + x
160 = 4x
Dividing both sides of the equation by 4 gives:
x = 160/4
x = 40
Therefore, the original angle measures 40 degrees, and the supplement of the angle measures 180 - 40 = 140 degrees.
Problem 2: The measures of an angle and its complement differ by 22 degrees. Find the measures of the angles.
Let's assume the measure of the angle is x degrees.
According to the problem, the angle and its complement (90 - x degrees) differ by 22 degrees:
x - (90 - x) = 22
Now, solve the equation to find the value of x:
x - 90 + x = 22
2x - 90 = 22
2x = 22 + 90
2x = 112
Dividing both sides of the equation by 2 gives:
x = 112/2
x = 56
Therefore, the original angle measures 56 degrees, and its complement measures 90 - 56 = 34 degrees.
I hope this helps! Let me know if you have any further questions.