8th Grade Angles in Triangles and Parallel Lines Test Solutions and Scoring (PDF)

8th Grade math test solutions: Angles in Triangles and Parallel Lines – Maths PDF

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This grade 8 angle relationships test answers for 8th Grade covers angles in triangles and parallel lines (Common Core 8.G.A.5), with a free PDF to print.

Use this answer key to score the angles in triangles and parallel lines test out of 20 points. Each solution shows the full work and a scoring guide, so partial credit can be given fairly when a student shows correct steps but makes an arithmetic slip.

Grade 8 · Common Core State Standards: 8.G.A.5

Grade 8 angle relationships test answers: worked solutions

Question 1 – Triangle angles [3 pts]

Third angle 55°, exterior angle 125°. Not drawn to scale.

\(180 – 52 – 73 = 55\). Exterior angle: \(52 + 73 = 125\).

Scoring: 1 point for the equation, 1 point for 55°, 1 point for 125°.

Question 2 – Solve for x [3 pts]

\(6x = 180\), so \(x = 30\). Angles: 30°, 75°, 75°.

Scoring: 1 point for the equation, 1 point for x, 1 point for the angles.

Question 3 – Parallel lines [3 pts]

The angle at the lower crossing in the upper-right position is a corresponding angle to the 58° angle, so it is 58°.

The marked angle forms a linear pair with it: 180 – 58 = 122.

122°

Scoring: 1 point for 58°, 1 point for the linear pair, 1 point for 122°.

Question 4 – Equation with angles [3 pts]

Both angles are 65° when x = 25.

Corresponding angles: \(2x + 15 = 65\), so \(x = 25\).

Scoring: 1 point for the relationship, 1 point for the equation, 1 point for 25.

Question 5 – Similar triangles [3 pts]

Triangle 1 third angle: 55. Triangle 2 third angle: 35. Both have angles 35, 55, 90, so they are similar (AA).

Scoring: 1 point for each third angle, 1 point for the conclusion.

Question 6 – Exterior angle [2 pts]

\(118 – 49 = 69\).

Scoring: 1 point for the theorem, 1 point for 69°.

Question 7 – Linear pair [1 pt]

\(x + (3x – 20) = 180\), so \(4x = 200\) and \(x = 50\). The other angle is \(3 \cdot 50 – 20 = 130\).

50° and 130°

Scoring: 1 point for both angles.

Question 8 – Explain [2 pts]

Two right angles add to 180°, leaving 0° for the third angle, which is impossible.

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

Total score

Total

20 points

Key facts behind this grade 8 angle relationships test answers

Key facts

Angles of a triangle: \(a + b + c = 180^{\circ}\).
Exterior angle = sum of the two remote interior angles.
Parallel lines: corresponding and alternate interior angles are equal.
Co-interior angles add to \(180^{\circ}\); vertical angles are equal.
Two equal angles are enough to show two triangles are similar (AA).

How to use this grade 8 angle relationships test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 8 chapters: Grade 8 math.

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