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

1 Complement and supplement ★★★

Find the complement and the supplement of \(38^\circ\).

2 Sorting pairs ★★★

For each pair, write complementary, supplementary, or neither.

1. \(18^\circ\) and \(72^\circ\)
2. \(110^\circ\) and \(70^\circ\)
3. \(44^\circ\) and \(47^\circ\)
4. \(120^\circ\) and \(60^\circ\)

3 Crossing lines ★★★

Two lines cross and one angle measures \(72^\circ\). Find the measures of the angles \(a\), \(b\) and \(c\).

4 Can it be a triangle? ★★★

Decide whether each set of lengths (in inches) can be the sides of a triangle.

1. 5, 6, 10
2. 2, 3, 7
3. 8, 8, 15
4. 4, 9, 13

5 Name the cross section ★★★

Name the shape of each cross section.

1. A cube cut by a plane parallel to one face.
2. A cylinder cut by a plane parallel to its bases.
3. A sphere cut by any plane.
4. A cone cut by a plane through its tip, perpendicular to its base.

6 Angles on a line ★★★

Three angles sit side by side on a straight line. Two of them measure \(40^\circ\) and \(75^\circ\), as in the figure. Find \(x\).

7 The leaning ladder ★★★

A ladder leans against a vertical wall on level ground. The ladder makes an angle of \(74^\circ\) with the ground. What angle does it make with the wall?

8 A supplementary equation ★★★

Two angles measuring \((x+14)^\circ\) and \((2x-5)^\circ\) are supplementary. Find \(x\) and both angles.

9 Vertical angles with variables ★★★

Two lines cross. A pair of vertical angles measure \((4x-7)^\circ\) and \((2x+21)^\circ\). Find \(x\) and the angle measure.

10 One angle four times the other ★★★

Two supplementary angles are such that one is 4 times the other. Find them.

11 Twenty degrees more ★★★

Two complementary angles differ by \(20^\circ\). What are they?

12 Range for the third side ★★★

A triangle has two sides of 9 cm and 14 cm. Write an inequality for the third side \(s\), and count how many whole-number lengths are possible.

13 Craft sticks ★★★

Dana has sticks of length 12 cm and 7 cm and wants a third stick to make a triangle. She can choose 4 cm, 6 cm, 18 cm or 19 cm. Which choices work?

14 How many triangles? ★★★

For each description, say whether there is no triangle, exactly one triangle, or many different triangles.

1. Sides 5 cm, 5 cm and 12 cm.
2. Sides 6 cm, 8 cm and 10 cm.
3. Angles \(30^\circ\), \(60^\circ\) and \(90^\circ\) only.
4. Sides 7 cm and 9 cm with a \(40^\circ\) angle between them.

15 Slicing a box ★★★

A shoe box is a rectangular prism 10 in long, 6 in wide and 4 in tall. Find the area of the cross section made by a cut parallel to (a) the \(10\times 6\) face and (b) the \(6\times 4\) face.

16 A linear pair in a crossing ★★★

Two lines cross. One angle is \((2x+10)^\circ\) and its neighbor is \((3x+20)^\circ\). Find both angles and the measure of the angle vertical to the first.

17 Three angles on a line ★★★

Three adjacent angles on a straight line measure \((x+10)^\circ\), \((2x-15)^\circ\) and \((3x+5)^\circ\). Find \(x\) and each angle.

18 Complement and supplement together ★★★

The complement of an angle is one fourth of its supplement. Find the angle.

19 Three times the complement ★★★

The supplement of an angle is three times its complement. Find the angle.

20 Sides with a variable ★★★

A triangle has side lengths \(x\), \(x+3\) and \(2x+1\) (in centimeters). Write the triangle inequalities, solve them, and find the smallest whole-number \(x\) that works. Give the three side lengths for that value.

21 Construction plan ★★★

You must draw a triangle with a side of 8 cm, an angle of \(50^\circ\) at one end and an angle of \(60^\circ\) at the other end. (a) Find the third angle. (b) Describe the drawing steps. (c) Is the triangle unique?

22 Slicing a cone ★★★

A cone is 12 cm tall and its base has radius 5 cm. A plane parallel to the base cuts the cone halfway up. The cross section is a circle with half the base radius. Find its radius and its area, to the nearest tenth of a square centimeter. Use \(\pi\approx 3.14159\).

23 The garden fence ★★★

A triangular garden has two sides of 15 m and 8 m. The third side is a whole number of meters. Marcus has at most 40 m of fencing for the whole perimeter. How many different lengths of the third side \(s\) are possible?