Testinar Grade 4 math

Angle Measure with Reference to a Circle

Students will connect angle measure to a fraction of a full circular turn.

CH07-06 Measurement, Data, and Angles

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

A full turn around a circle measures how many degrees?
1. 90°
2. 180°
3. 270°
4. 360°
How many degrees is a half turn around a circle?
1. 90°
2. 180°
3. 270°
4. 360°
A quarter turn around a circle measures how many degrees?
1. 45°
2. 90°
3. 180°
4. 270°
How many degrees is a three-quarter turn around a circle?
1. 90°
2. 180°
3. 270°
4. 360°
If you turn \(\frac{1}{6}\) of the way around a circle, how many degrees do you turn?
1. 60°
2. 90°
3. 120°
4. 180°
Turning \(\frac{1}{3}\) of the way around a circle equals how many degrees?
1. 60°
2. 120°
3. 180°
4. 240°
If you turn \(\frac{1}{12}\) of the way around a circle, how many degrees do you turn?
1. 20°
2. 30°
3. 45°
4. 60°
What is the measure of angle \(\theta\) shown in the diagram?
1. 30°
2. 45°
3. 60°
4. 90°

Teacher and parent reference

Answer key and explanations

D. 360°
A complete rotation around a circle measures \(\mathbf{360°}\) because that's the universal standard for a full turn.
B. 180°
A half turn is \(\frac{1}{2}\) of the full circle: \(\frac{1}{2} \times 360° = \mathbf{180°}\).
B. 90°
A quarter turn is \(\frac{1}{4}\) of the full circle: \(\frac{1}{4} \times 360° = \mathbf{90°}\).
C. 270°
A three-quarter turn is \(\frac{3}{4}\) of the full circle: \(\frac{3}{4} \times 360° = \mathbf{270°}\).
A. 60°
One-sixth of the circle is \(\frac{1}{6} \times 360° = \mathbf{60°}\).
B. 120°
One-third of the circle is \(\frac{1}{3} \times 360° = \mathbf{120°}\).
B. 30°
One-twelfth of the circle is \(\frac{1}{12} \times 360° = \mathbf{30°}\), which matches the spacing between hour marks on a clock.
C. 60°
The diagram shows an angle between a vertical and a slanted ray. The arc sweeps \(\mathbf{60°}\) from one ray to the other.