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

1 Complementary and supplementary / 3 pts

1. Find the complement of \(56^\circ\).
2. Find the supplement of \(56^\circ\).
3. Are \(38^\circ\) and \(62^\circ\) complementary? Explain.

2 Vertical angles / 4 pts

Two lines cross. Two vertical angles measure \((6x-4)^\circ\) and \((4x+22)^\circ\).

1. Find \(x\).
2. Find the measure of these two angles.
3. Find the measure of the other two angles.

3 Angles on a line / 3 pts

Three adjacent angles on a straight line measure \((x+5)^\circ\), \((2x)^\circ\) and \((3x-11)^\circ\). Write an equation, solve it, and give the three angles.

4 Triangle inequality / 4 pts

1. Can 6 cm, 9 cm and 14 cm be the sides of a triangle?
2. Can 5 cm, 7 cm and 12 cm?
3. Can 3 cm, 10 cm and 8 cm?
4. Two sides of a triangle are 8 cm and 13 cm. Give the range of the third side.

5 Unique triangle? / 3 pts

Say whether each description gives no triangle, exactly one, or many.

1. Sides 4 cm, 6 cm and 11 cm.
2. Angles \(20^\circ\), \(70^\circ\) and \(90^\circ\) only.
3. Sides 5 cm and 7 cm with a \(50^\circ\) angle between them.

6 Cross sections / 3 pts

A rectangular prism measures 8 cm by 5 cm by 3 cm, and a sphere has radius 6 cm.

1. What shape is the cross section of the prism cut parallel to the \(8\times 5\) face?
2. Find its area.
3. A plane cuts the sphere through its center. Find the area of the cross section in terms of \(\pi\), then to the nearest tenth. Calculator allowed.