MathematicsFreePrintable

Exploring Angle Relationships

A free mathematics worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Exploring Angle Relationships

A mini-golf course is being planned for a community park. Use angle clues to check the turns, ramps and paths. Show working where you can. Remember: a right angle is 90°, a straight angle is 180° and a full turn is 360°.

Angle Spotters

Classify each angle as acute, right, obtuse or straight. An acute angle is less than 90°; an obtuse angle is between 90° and 180°.

1.The first path turn is 42°. What type of angle is it?

2.A ramp meets the ground at 90°. Choose its angle type.

Acute
Right
Obtuse
Straight

3.One bend in the path measures 135°. What type of angle is it?

Find the Missing Turns

Use angle facts to help finish the course plan. Angles on a straight line total 180°. Angles around a point total 360°. Opposite angles made by two intersecting lines are equal.

4.Two paths cross. One angle is 68°. Find the angle directly opposite it, then the two neighbouring angles.

5.At a straight path junction, the two angles are 73° and x°. Work out x.

6.A circular putting green has three marked sectors: 110°, 140° and x°. Find x, the angle of the final sector.

Angle Pairs and Design

Some angle pairs fit together to make a larger turn. Complementary angles add to 90°; supplementary angles add to 180°.

7.A pair of ramp supports make complementary angles. One is 34°. What is the other angle?

8.Two adjoining path turns are supplementary. One turn is 125°. Is the other turn 55°, 65° or 75°? Explain with a calculation.

9.A gate opens from closed to fully open through a quarter-turn. It has opened 38°. How many more degrees must it turn to reach a right angle?

10.Draw two straight lines crossing to make an X. Label one angle 40°, then write the sizes of the other three angles. Use the opposite-angle and straight-line facts.

11.Course designers want to split a 180° straight path junction into three angles: 45°, 65° and x°. Find x and name its angle type.