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Triangle Angle Sum - Problem 2

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

Recall that by the triangle angle sum theorem, the sum of the measures of the angles in a triangle is 180°. Using this fact, it is possible to find the value of a variable. When the angles of a triangle are given by expressions with variables, add these expressions together. By the triangle angle sum theorem, their sum should be equal to 180°. So, set their sum equal to 180°, and then, with algebra techniques, solve for the variable.

You can use algebraic techniques of solving and apply it to the triangle angle sum, which says that thee angles in a triangle must always sum to 180 degrees. That’s a theory that you’re going to be using the rest of geometry.

So if we look at this problem right here, we have three angles that all are in terms of a variable x. so I can write that these three angles once summed equal 180 degrees. So let’s write that equation starting with 2x minus 3 that quantity plus your next angle, 3x plus 8 plus your last angle which is 5x and I know that these one, two, three angles must add up to 180 degrees. So now it just becomes a simple algebraic equation. If I combine like terms, I can combine 2x, 3x and 5x and I get 10x. I can combine -3 and +8 and I get +5. And that’s going to equal 180 degrees.

Last step before diving is to subtract five, so we get 10x equals 175, and I’m going to divide by 10, and I see that x must be 17.5. So find x, x equals 17.5 where the key, just wanted to make sure that’s clear, the key to this problem was realizing that the sum of these three angles was 180 degrees.

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