if the measure of an angle exceeds four times the measure of its complement by 25, what is the measure of the angle?
x = 4(90-x)+25
x = 77
check:
77 = 4(13)+25
Well, let's solve this equation together. Let's call the measure of the angle "x." The complement of the angle would be 90 degrees minus x, right?
According to the problem, "the measure of an angle exceeds four times the measure of its complement by 25." In equation form, that would be x = 4(90 - x) + 25.
Now, let's simplify that equation and solve for x.
x = 4(90 - x) + 25
x = 360 - 4x + 25
5x = 385
x = 77
So, the measure of the angle is 77 degrees.
To solve this problem, let's first review what a complement of an angle is. The complement of an angle is another angle that, when added to the original angle, forms a right angle, which measures 90 degrees.
Let's assume the measure of the angle is x degrees. The complement of the angle would then be (90 - x) degrees.
According to the problem, the measure of the angle exceeds four times the measure of its complement by 25. Mathematically, this can be represented as:
x = 4(90 - x) + 25
To solve for x, let's simplify the equation step by step:
x = 360 - 4x + 25
x + 4x = 360 + 25
5x = 385
x = 385/5
x = 77
Therefore, the measure of the angle is 77 degrees.