Question

Identifying Angle Relationships
Jack is framing the roof of a structure using a triangle and two exterior angles.

A triangle has angles a degrees, b degrees, and c degrees. The exterior angle to a degrees is x degrees.

Which relationships about the interior and exterior angles are true? Check all that apply.
a° + b° + c° = 180°
x° + a° = 180°
a° = c°
a° + c° = 90°
x° + a° = b° +

Answer 1

Correct statements:
- a + b + c = 180° — True. (Sum of interior angles of a triangle.)
- x + a = 180° — True. (Exterior angle and its adjacent interior angle are supplementary.)
- a = c — False (only true for an isosceles triangle with those equal).
- a + c = 90° — False (only true if b = 90°).
- x + a = b + c — False. (Since x = b + c, x + a = a + b + c = 180°, which is not equal to b + c in general.)

Also useful: x = b + c (the exterior-angle theorem).