find angle a - pre algebra math

angle A is 30˚

We know that angle A is x + 37, the other unknown angle is x + 67, and the known angle is 90˚

When you add the angles of a triangle, they always equal 180˚. This means that when you have a 90˚, the other two angles equal 180 – 90 = 90. So, to calculate this problem you have to solve the following equation for x:

x + 37 + x + 67 = 90

To solve this, first we have to combine like terms, in order to simplify it a bit. The like terms in this equation are x and x, and the non–variable values.

So, the equation becomes x + x + 37 + 67, which can be further simplified to 2x + 104 = 90

From there, we must further undo the equation, first by subtracting 104 from both sides to eliminate it and further isolate the variable.

2x + 104 – 104 = 90 – 104

2x = –14

Then, we divide both sides by 2 to completely isolate the variable.

2x ÷ 2 = –14 ÷ 2          x = –7

Now, finding angle A is easy. We know x, so we can substitute the value in x + 37 to find the angle's measurements.  –7 + 37 = 30, so angle A = 30˚

And we can further check this by finding the other unknown angle: –7 + 67 = 60, and 90 + 60 = 150      180 – 150 = 30