Parallel Lines Angles Worksheet Answer Key – Grade 8

Problem 1 Third angle

180 − (48 + 73) = 180 − 121 = 59.

The third angle is 59°.

Problem 2 Right triangle

The angles total 180° and the right angle is 90°, so the acute angles total 90°.

90 − 37 = 53°

Problem 3 Isosceles apex

The base angles are equal and share 180 − 40 = 140.

140 ÷ 2 = 70.

Each base angle is 70°.

Problem 4 Exterior angle

The exterior angle equals the sum of the remote interior angles: 52 + 64 = 116.

116°

Problem 5 Vertical and adjacent

Vertical angles are equal, so the vertical angle is 128°.

Adjacent angles form a linear pair: 180 − 128 = 52.

Vertical angle 128°; adjacent angle 52°

Problem 6 Corresponding angles

The marked angles are in the same position at the two intersections, so they are corresponding angles. Parallel lines make them equal.

x = 112°; corresponding angles

Problem 7 Alternate interior

The marked angles lie between the lines on opposite sides of the transversal: alternate interior angles. They are equal.

y = 74°

Problem 8 Same-side interior

The two angles share a straight angle of 180°: 180 − 143 = 37.

37°

Problem 9 Triangle with x

(x + 10) + (2x − 5) + (3x + 13) = 180, so 6x + 18 = 180 and x = 27.

Angles: 27 + 10 = 37; 2 · 27 − 5 = 49; 3 · 27 + 13 = 94. Check: 37 + 49 + 94 = 180.

x = 27; angles 37°, 49°, 94°

Problem 10 Exterior with x

5x − 12 = (x + 20) + (2x + 10) = 3x + 30.

2x = 42, so x = 21. The exterior angle is 5 · 21 − 12 = 93. Check: 41 + 52 = 93.

x = 21; exterior angle 93°

Problem 11 Parallel with x

3x + 8 = 5x − 22, so 30 = 2x and x = 15.

3 · 15 + 8 = 53 and 5 · 15 − 22 = 53.

x = 15; each angle is 53°

Problem 12 Same-side with x

(7x − 5) + (3x + 15) = 180, so 10x + 10 = 180 and x = 17.

7 · 17 − 5 = 114 and 3 · 17 + 15 = 66, which add to 180.

x = 17; angles 114° and 66°

Problem 13 All eight angles

∠1 is vertical to the 58° angle: 58°. ∠2 and ∠3 are linear partners of 58°: 180 − 58 = 122°.

∠4 corresponds to ∠1: 58°. ∠5 and ∠6 correspond to ∠2 and ∠3: 122°. ∠7 corresponds to the 58° angle: 58°.

∠1 = 58°, ∠2 = 122°, ∠3 = 122°, ∠4 = 58°, ∠5 = 122°, ∠6 = 122°, ∠7 = 58°

Problem 14 Parallel or not?

(a) Corresponding angles must be equal for parallel lines. 67° ≠ 69°, so the lines are not parallel.

(b) Equal alternate interior angles show that the lines are parallel.

(a) Not parallel; (b) parallel

Problem 15 AA similarity

Third angle of △ABC: 180 − 44 − 79 = 57°. Third angle of △DEF: 180 − 79 − 57 = 44°.

Both triangles have angles 44°, 57°, and 79°. Two pairs of equal angles are enough (AA).

Yes, the triangles are similar by AA

Problem 16 Roof truss

180 − 104 = 76 is shared by the two equal base angles.

76 ÷ 2 = 38.

38° each

Problem 17 Parallel streets

The upper right angle at Elm corresponds to the upper right angle at Oak, which is 123°.

The lower left angle at Oak is vertical to that angle, so it is also 123°.

Check with a linear pair: its neighbor measures 57° and 123 + 57 = 180.

y = 123°

Problem 18 Garden angles

Let the angles be 3k, 4k, and 5k. Then 12k = 180 and k = 15.

3 · 15 = 45; 4 · 15 = 60; 5 · 15 = 75.

45°, 60°, 75°

Problem 19 Find the interior angle

The exterior angle at C equals ∠A + ∠B: 7x − 20 = (2x + 3) + (3x − 7) = 5x − 4.

2x = 16, so x = 8. ∠A = 19°, ∠B = 17°, exterior angle = 36°.

Interior angle at C: 180 − 36 = 144. Check: 19 + 17 + 144 = 180.

x = 8; ∠C = 144°

Problem 20 Why 180?

Alternate interior angles match, so ∠A = 47° and ∠C = 68°.

The three angles that meet at B along the straight line total 180°: ∠ABC = 180 − 47 − 68 = 65.

So ∠A + ∠B + ∠C = 47 + 65 + 68 = 180, because the three angles at B match the three angles of the triangle.

∠ABC = 65°