Question

Triangle ABC is a right triangle.

Triangle A B C. Angle A is x degrees, B is 90 degrees, C is (x minus 10) degrees. The exterior angle to angle C is (2 x + 40) degrees.

Which equations can be used to find the value of x? Check all that apply.
x + 90 + (x minus 10) = 180
x + 90 + (2 x + 40) = 180
2 x + 80 = 180
x + 90 = 2 x + 40
(x minus 10) + 90 = 2 x + 40

Answer 1

Correct:
- x + 90 + (x − 10) = 180 (interior angles sum to 180)
- 2x + 80 = 180 (simplification of the above)

Also valid:
- x + 90 = 2x + 40 (exterior angle = sum of the two remote interior angles)

Not valid:
- x + 90 + (2x + 40) = 180 (you cannot add an exterior angle with the other two to get 180)
- (x − 10) + 90 = 2x + 40 (exterior equals the two remote interiors, not an adjacent interior plus the right angle)