Angle Relationships: Grade 7 Math Test Answer Key – PDF Download

Question 1: Complement and supplement (2 points)

1. \(90-64=26\): \(26^{\circ}\)
2. \(180-64=116\): \(116^{\circ}\)

Scoring: 1 point per part. Award no point if the two totals (90 and 180) are swapped.

Question 2: Vertical angles (2 points)

1. Angle \(a\) is supplementary to \(48^{\circ}\): \(180-48=132\). \(a=132^{\circ}\)
2. Angle \(b\) is vertical to \(48^{\circ}\), so \(b=48^{\circ}\). Angle \(c\) is vertical to \(a\), so \(c=132^{\circ}\).

Scoring: 1 point for \(a\); 1 point for both \(b\) and \(c\).

Question 3: Equation on a line (2 points)

1. \(5x+4x=180\), so \(9x=180\) and \(x=20\).
2. The larger angle is \(5(20)=100\): \(100^{\circ}\). The other angle is \(4(20)=80\), and \(100+80=180\).

Scoring: 1 point for the correct equation and \(x\); 1 point for \(100^{\circ}\).

Question 4: Complementary equation (3 points)

1. \((x+14)+(2x-5)=90\), so \(3x+9=90\), \(3x=81\), and \(x=27\).
2. \(27+14=41\) and \(2(27)-5=49\). Check: \(41+49=90\). \(41^{\circ}\) and \(49^{\circ}\)

Scoring: part (a) 1 point for the equation and 1 point for \(x\); part (b) 1 point for both angles.

Question 5: Vertical angles equation (3 points)

1. Vertical angles are equal: \(4x+14=6x-8\). Then \(22=2x\), so \(x=11\). Check: \(4(11)+14=58\) and \(6(11)-8=58\).
2. Angle \(y\) is supplementary to \(58^{\circ}\): \(180-58=122\). \(y=122^{\circ}\)

Scoring: 1 point for the equation, 1 point for \(x\), 1 point for \(y\).

Question 6: Checking a claim (2 points)

1. No. \(70+100=170\), and supplementary angles must add up to \(180^{\circ}\).
2. \(180-70=110\): \(110^{\circ}\)

Scoring: 1 point for showing the sum is 170 and not 180; 1 point for \(110^{\circ}\).

Question 7: Road intersection (3 points)

1. The angles are supplementary: \((2x+20)+(x+10)=180\).
2. \(3x+30=180\), so \(3x=150\) and \(x=50\).
3. \(2(50)+20=120\) and \(50+10=60\). Check: \(120+60=180\). \(120^{\circ}\) and \(60^{\circ}\)

Scoring: 1 point per part.

Question 8: Three angles on a line (3 points)

1. \(x+(x+25)+(2x+15)=180\)
2. \(4x+40=180\), so \(4x=140\) and \(x=35\).
3. The angles are \(35\), \(60\), and \(85\); check \(35+60+85=180\). The largest is \(85^{\circ}\).

Scoring: 1 point per part.

⬇ Download the Grade 7 Angle Relationships test answer key (PDF, 111 KB)

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