Two angles are complementary. Their difference is 50^*. Find the angles.
70 and 20
Well, it seems these angles can't get along because their difference is causing quite a temperature rise of 50 degrees! Don't worry, I'm here to help. Let's call one angle x and the other angle y. Since they are complementary, we know that x + y = 90 degrees.
Now, we're also given that their difference is 50 degrees, so we can set up another equation: x - y = 50 degrees.
Now we have a system of equations! Let's solve it.
We can use the elimination method by adding the two equations together. When we do that, the y's will cancel out and we'll be left with 2x = 140 degrees.
Dividing both sides by 2, we find that x = 70 degrees.
To find y, we can substitute this value back into one of the original equations. If we use x + y = 90, we'll have 70 + y = 90. Subtracting 70 from both sides gives us y = 20 degrees.
So, the two complementary angles are 70 degrees and 20 degrees. I hope they can find some common ground and start complementing each other better!
Let's assume that one of the angles is x (in degrees). Since the two angles are complementary, the other angle would be 90 - x degrees.
We can set up the equation as follows:
90 - x - x = 50
Simplifying the equation:
90 - 2x = 50
Subtracting 90 from both sides:
-2x = 50 - 90
Simplifying further:
-2x = -40
Dividing both sides of the equation by -2 to isolate x:
x = -40 / -2
Simplifying:
x = 20
Therefore, one angle is 20 degrees, and the other angle can be found by subtracting this from 90:
90 - 20 = 70
So, the two angles are 20 degrees and 70 degrees.
To find the angles, let's start by defining the given information. We have two angles that are complementary, which means they add up to 90 degrees. Let's call these angles A and B.
The problem states that the difference between the angles is 50 degrees. Mathematically, we can express this as:
A - B = 50
Since the angles are complementary, we also know that:
A + B = 90
To solve this system of equations, we can use a method called substitution. We can rearrange the second equation to express one variable in terms of the other. Let's solve for A:
A = 90 - B
Now we can substitute this expression for A in the first equation:
(90 - B) - B = 50
Simplifying this equation, we get:
90 - 2B = 50
Now, we can isolate the B term by subtracting 90 from both sides:
-2B = 50 - 90
-2B = -40
Dividing both sides by -2:
B = (-40) / (-2)
B = 20
Now that we have found the measure of angle B, we can substitute this value back into one of the original equations to find angle A:
A + 20 = 90
A = 90 - 20
A = 70
Therefore, the two angles are 70 degrees and 20 degrees.