Parallel Lines Angles Test Answer Key with Scoring – Grade 8

Question 1 Triangle and exterior (2 points)

(a) 180 − 63 − 54 = 63°

(b) The exterior angle equals 63 + 54 = 117°. Check: 180 − 63 = 117.

Scoring: 1 point per part.

Question 2 Find three angles (3 points)

(a) a is vertical to the 126° angle: a = 126°.

(b) b and the 126° angle are corresponding angles: b = 126°.

(c) c forms a linear pair with b: 180 − 126 = c = 54°.

Scoring: 1 point for each correct angle with a valid reason.

Question 3 Equation with parallel lines (3 points)

Alternate interior angles are equal: 6x − 14 = 4x + 16.

2x = 30, so x = 15.

6 · 15 − 14 = 76 and 4 · 15 + 16 = 76.

x = 15; each angle is 76°

Scoring: 1 point for the equation, 1 point for the value of x, 1 point for the angle measure.

Question 4 Triangle with unknowns (3 points)

(x + 8) + (2x − 4) + (3x + 2) = 180, so 6x + 6 = 180 and x = 29.

Angles: 37°, 54°, 89°. Check: 37 + 54 + 89 = 180.

x = 29; angles 37°, 54°, 89°

Scoring: 1 point for the equation, 1 point for the value of x, 1 point for the three angles.

Question 5 Exterior angle problem (3 points)

(a) The exterior angle equals the sum of the remote interior angles: 138 = 49 + ∠R, so ∠R = 89°.

(b) ∠PQR and the exterior angle form a linear pair: 180 − 138 = 42°. Check: 49 + 42 + 89 = 180.

Scoring: part (a) 1 point for the equation, 1 point for the answer; part (b) 1 point.

Question 6 Similar triangles (2 points)

Third angle of triangle 1: 180 − 35 − 80 = 65°. Third angle of triangle 2: 180 − 80 − 65 = 35°.

Yes, both have angles 35°, 65°, and 80°, so they are similar by AA

Scoring: 1 point for both third angles, 1 point for the conclusion.

Question 7 Are the lines parallel? (2 points)

For parallel lines, same-side interior angles add to 180°. Here 112 + 78 = 190.

No, the lines are not parallel

Scoring: 1 point for the sum, 1 point for the conclusion.

Question 8 Skate ramp (2 points)

Top angle: 180 − 90 − 18 = 72°.

The exterior angle at the top equals the sum of the remote angles: 90 + 18 = 108°, or 180 − 72 = 108°.

Top angle 72°; exterior angle 108°

Scoring: 1 point per angle.