Angles and Geometric Constructions: math test solutions, Grade 7 – download the PDF

1 Complementary and supplementary / 3 pts

1. \(90-56=34\), so \(34^\circ\). (1 pt)
2. \(180-56=124\), so \(124^\circ\). (1 pt)
3. \(38+62=100\), not \(90\): no. (1 pt)

2 Vertical angles / 4 pts

1. \(6x-4=4x+22\), so \(2x=26\) and \(x=13\). (2 pts)
2. \(6(13)-4=74\), so each measures \(74^\circ\). (1 pt)
3. \(180-74=106\), so each measures \(106^\circ\). (1 pt)

3 Angles on a line / 3 pts

\((x+5)+2x+(3x-11)=180\), so \(6x-6=180\). (1 pt)

\(6x=186\), so \(x=31\). (1 pt)

The angles are \(36^\circ\), \(62^\circ\) and \(82^\circ\); check \(36+62+82=180\). (1 pt)

4 Triangle inequality / 4 pts

1. \(6+9=15>14\): yes. (1 pt)
2. \(5+7=12\), not greater than 12: no. (1 pt)
3. \(3+8=11>10\): yes. (1 pt)
4. \(13-8

5 Unique triangle? / 3 pts

1. \(4+6=10<11\): none. (1 pt)
2. Angles only: many triangles of different sizes. (1 pt)
3. Two sides and the included angle: exactly one. (1 pt)

6 Cross sections / 3 pts

1. A rectangle, 8 cm by 5 cm. (1 pt)
2. \(8\times 5=40\text{ cm}^2\). (1 pt)
3. A circle of radius 6 cm: \(\pi\times 6^2=36\pi\approx 113.1\text{ cm}^2\). (1 pt)