Angles, Parallel Lines and Triangles: Grade 8 Math Test Answer Key – PDF Download

Question 1: Third angle (2 points)

1. \(180-63-49=68\): \(68^{\circ}\).
2. \(180-90-28=62\): \(62^{\circ}\).

Scoring: 1 point for each correct angle.

Question 2: Triangle with variables (2 points)

1. \((x+15)+2x+(3x-15)=6x=180\), so \(x=30\).
2. \(45\), \(60\) and \(75\): \(45^{\circ}\), \(60^{\circ}\), \(75^{\circ}\). Check: \(45+60+75=180\).

Scoring: 1 point for \(x=30\) with the equation; 1 point for all three angles.

Question 3: Exterior angles (2 points)

1. \(x=55+48=103\): \(x=103^{\circ}\).
2. \(142-89=53\): \(53^{\circ}\).

Scoring: 1 point for each part.

Question 4: Parallel lines and a transversal (3 points)

1. \(x\) and \(72^{\circ}\) are alternate interior angles: \(x=72^{\circ}\).
2. \(y\) and \(72^{\circ}\) are corresponding angles: \(y=72^{\circ}\).
3. \(z\) and \(72^{\circ}\) are same-side interior angles, so \(z=180-72=108\): \(z=108^{\circ}\).

Scoring: for each part, 1 point for the correct measure with the correct relationship named.

Question 5: Alternate interior with x (2 points)

1. Alternate interior angles are equal: \(4x-12=2x+18\), so \(2x=30\) and \(x=15\).
2. \(4(15)-12=48\) and \(2(15)+18=48\): \(48^{\circ}\) each.

Scoring: 1 point for the equation and \(x=15\); 1 point for \(48^{\circ}\).

Question 6: Roof truss (2 points)

1. \(112+2x=180\), so \(2x=68\) and \(x=34^{\circ}\).
2. \(y=180-34=146\), or \(34+112=146\): \(y=146^{\circ}\).

Scoring: 1 point for each part.

Question 7: Similar by angles (2 points)

1. \(\triangle ABC\): \(180-35-80=65\). \(\triangle DEF\): \(180-80-65=35\). \(65^{\circ}\) and \(35^{\circ}\).
2. Both triangles have angles \(35^{\circ}\), \(65^{\circ}\) and \(80^{\circ}\). Yes, they are similar by the AA criterion.

Scoring: 1 point for both third angles; 1 point for yes with the reason.

Question 8: Missing side by AA (2 points)

1. The triangles are similar by AA, and \(DE: AB=12: 8=\frac{3}{2}\): \(k=\frac{3}{2}\).
2. \(DF=10\cdot\frac{3}{2}=15\): \(DF=15\).

Scoring: 1 point for each part.

Question 9: Why the angle sum is 180 (3 points)

1. \(x\) and \(\angle A\) are alternate interior angles, so \(x=49^{\circ}\). \(z\) and \(\angle B\) are alternate interior angles, so \(z=63^{\circ}\).
2. \(\angle C=180-49-63=68\). Along the line: \(49+68+63=180\). \(\angle C=68^{\circ}\).

Scoring: part (a) 1 point for each of \(x\) and \(z\) with the relationship named; part (b) 1 point for \(\angle C\) with the sum shown.

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