Angle and Triangle Theorems

The results a proof is built from.

12 problems · about 21 minutes · G-CO.C.9, G-CO.C.10

What this lesson teaches

The student applies angle relationships and triangle theorems in short proofs.

Vertical angles are equal; angles on a line are supplementary.
Parallel lines make corresponding and alternate angles equal.
A triangle totals 180°, and an exterior angle equals the two opposite interior ones.

Straightforward practice. Get the method working first.

5 problems

A triangle has angles 80° and 55°. What is the third, in degrees?
Answer 45
Why 45°.
What does an exterior angle equal?
Answer The sum of the two opposite interior angles.
Why The two non-adjacent interior angles added.
An angle is 35°. Its complement, in degrees?
Answer 55
Why 90 − 35.
An angle is 140°. Its supplement, in degrees?
Answer 40
Why 180 − 140.
A triangle has angles 90° and 35°. The third, in degrees?
Answer 55
Why 180 − 125.

The same ideas with more to keep track of.

3 problems

Interior angles 45° and 65°. The exterior angle at the third vertex, in degrees?
Answer 110
Why Add the two opposite ones.
One vertical angle is 72°. What is the other, in degrees?
Answer 72
Why They are equal.
An isosceles triangle has an apex angle of 40°. Each base angle, in degrees?
Answer 70
Why 140 shared between two.

Mixed problems. Work out what kind of question it is before you start.

4 problems

Sort each angle pair by whether they are equal or supplementary.
Answer Equal: Vertical angles, Corresponding angles on parallel lines · Supplementary: Co-interior angles on parallel lines, Angles on a straight line
Why Two of these total 180°.
A triangle has two angles of 60°. The third, in degrees?
Answer 60
Why 180 − 120.
The Third Angle: A triangle has angles 50° and 60°. What is the third, in degrees?
Answer 70 degrees
Why 70°.
The Supplement: An angle is 110°. What is its supplement, in degrees?
Answer 70 degrees
Why 70°.