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Topic: **Exterior homeworks****Question:**
I'm doing this geometry homework and when I solve for x of the exterior angle and then add up all the angles of the triangle, it doesn't add up to 180. I've done like 4 of them and they don't add up to 180!
Here's an example:
The sides of a triangle are 80 degrees, x degrees, and the exterior angle is (3x-22) degrees. There's nothing next to the exterior angle, it's at the top of the triangle, and the other two measurements are at the bottom corners of the triangle.
I keep on getting that x = 51 and that the exterior angle equals 131 degrees but then when you add 80, 51, and 131, that does not equal 180.
I'm so stressed. What am I doing wrong?!

June 19, 2019 / By Cybill

If you have a line of slope m, and θ is the angle it makes with the x-axis, then tan(θ) = m. So you can use tan^-1(m), the inverse tangent (sometimes written as the arctangent, "arctan(m)"), to find the degree measure. This is because if you draw a right triangle from the angle, the rise/run ratio is the same as the side opposite of the angle divided by the adjacent side. This is the tangent function in trigonometry. For example, if you have a line of slope 1, then the angle it makes is tan^-1(1) = 45 degrees. Most scientific calculators will have an inverse tangent function. Microsoft Excel also has an ATAN(number) function, though it gives the result in radians. You have to convert it to degrees by entering "=+DEGREES(ATAN(1))" for example to get back 45.

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