Find the measure of an angle , if 7 times its complement is 10 less than three times its supplement
let the angle be x
its complement is 90-x
its supplement is 180-x
7(90-x) = 3(180-x) - 10
solve for x
so much thanks
Must solve the sum in detail
To find the measure of an angle, let's assign a variable to it. Let's call the angle "x".
The complement of an angle is the angle that, when added to the given angle, will result in a right angle (90 degrees). The complement of angle "x" would be (90 - x).
The supplement of an angle is the angle that, when added to the given angle, will result in a straight line (180 degrees). The supplement of angle "x" would be (180 - x).
According to the given information, 7 times the complement of the angle is 10 less than three times its supplement. We can write this as an equation:
7(90 - x) = 3(180 - x) - 10
Let's solve this equation to find the value of "x".
First, distribute on both sides of the equation:
630 - 7x = 540 - 3x - 10
Combine like terms:
-7x + 3x = 540 - 10 - 630
-4x = -100
Divide both sides of the equation by -4:
x = (-100) / (-4)
x = 25
Therefore, the measure of the angle is 25 degrees.
Angle = 20
Complement = 70
Supplement = 160