an angle measuring 32 degrees has a complement that measures (2x-16) degrees. What is the value of x?
2x - 16 = 90 - 32
2x - 16 = 58
2x = 74
x = 37
Well, let's take a comedic angle on this problem!
If 32 degrees went on a blind date with its complement, what would they talk about? Probably their shared love for acute angles and hanging out with right angles.
Now, let's solve this puzzle. We know that the sum of an angle and its complement is always 90 degrees, because together they form a right angle. So, we can set up an equation:
32 + (2x - 16) = 90
Let's solve this equation to find the value of x:
2x - 16 = 90 - 32
2x - 16 = 58
2x = 74
x = 74/2
x = 37
So, x equals 37. Now, our angle measuring 32 degrees has found its complement! They'll make a great team.
The complement of an angle is the angle that, when added to the original angle, gives a total of 90 degrees.
So, we have the equation:
(original angle) + (complement) = 90
Given that the original angle measures 32 degrees and the complement measures (2x-16) degrees, we can plug these values into the equation:
32 + (2x-16) = 90
Simplifying the equation:
32 + 2x - 16 = 90
2x + 16 = 90
Subtracting 16 from both sides:
2x = 74
Dividing both sides by 2:
x = 37
Therefore, the value of x is 37.
To find the value of x, we need to use the concept of complementary angles.
Complementary angles are two angles whose measures add up to 90 degrees. In this case, the given angle measures 32 degrees, and its complement measures (2x - 16) degrees.
So, we can write the equation:
32 + (2x - 16) = 90
Now, let's solve the equation step by step:
First, simplify the equation by combining like terms:
2x + 16 + 32 = 90
Next, simplify further:
2x + 48 = 90
To isolate the variable, subtract 48 from both sides of the equation:
2x = 90 - 48
2x = 42
Finally, divide both sides of the equation by 2 to solve for x:
x = 42/2
x = 21
Therefore, x has a value of 21.