An angle measures 5 degrees more than 4 times its complement. What is the angle?
I understand that the formula would be 4x+5 degrees. Would this be the answer?
The sum of complementary angles = 90. Let x = the smaller angle.
x + 4x + 5 = 90
5x = 85
x = 17
Larger angle = 90 - 17
Well, if we let x represent the angle, then the complement of the angle would be 90 - x degrees. According to the problem, the angle measures 5 degrees more than 4 times its complement. So the equation would be x = 4(90 - x) + 5. Solving for x, we get x = 53 degrees. Therefore, the angle measures 53 degrees.
Yes, you are correct! The formula to represent the given information would be 4x + 5 degrees, where x is the measure of the complement angle. To find the angle, you can substitute the value of x into the formula and calculate.
Yes, you are correct that the formula to find the angle would be 4x + 5 degrees. However, your task is to find the actual value of the angle.
To solve this, we need to set up an equation. We know that an angle and its complement add up to 90 degrees (since the sum of all angles in a right triangle is 90 degrees). So, we can write the equation as follows:
angle + complement = 90 degrees
But we also know that the angle is 5 degrees more than 4 times its complement. So we can replace the angle in the equation with 4 times its complement plus 5 degrees:
4(complement) + 5 degrees + complement = 90 degrees
Now, we can solve this equation to find the value of the complement:
5(complement) + 5 degrees = 90 degrees
Subtracting 5 degrees from both sides:
5(complement) = 85 degrees
Dividing both sides by 5:
complement = 17 degrees
Now that we know the value of the complement, we can substitute it back into the equation to find the angle:
angle = 4(complement) + 5 degrees
angle = 4(17 degrees) + 5 degrees
angle = 68 degrees + 5 degrees
angle = 73 degrees
Therefore, the angle measures 73 degrees.