To solve these problems, we need to remember one key fact:
A full turn (a whole circle) is always $360^\circ$.
The instructions say the angles in each circle are "congruent," which means they are all equal in size. To find the measure of one angle, we divide $360$ by the number of slices in the circle.
Here is the step-by-step solution for each problem:
1.
* Count the slices: There are
5 equal slices.
* Calculate the angle: $360 \div 5 = 72$.
* So, each angle is $72^\circ$. It takes 5 of them to make a full turn.
2.
* Count the slices: There are
10 equal slices.
* Calculate the angle: $360 \div 10 = 36$.
* So, each angle is $36^\circ$. It takes 10 of them to make a full turn.
3.
* Count the slices: There are
4 equal slices.
* Calculate the angle: $360 \div 4 = 90$.
* So, each angle is $90^\circ$. It takes 4 of them to make a full turn.
4.
* Count the slices: There are
2 equal slices.
* Calculate the angle: $360 \div 2 = 180$.
* So, each angle is $180^\circ$. It takes 2 of them to make a full turn.
5.
* Count the slices: There are
9 equal slices.
* Calculate the angle: $360 \div 9 = 40$.
* So, each angle is $40^\circ$. It takes 9 of them to make a full turn.
6.
* Count the slices: There are
8 equal slices.
* Calculate the angle: $360 \div 8 = 45$.
* So, each angle is $45^\circ$. It takes 8 of them to make a full turn.
7.
* Count the slices: There are
3 equal slices.
* Calculate the angle: $360 \div 3 = 120$.
* So, each angle is $120^\circ$. It takes 3 of them to make a full turn.
8.
* Count the slices: There are
6 equal slices.
* Calculate the angle: $360 \div 6 = 60$.
* So, each angle is $60^\circ$. It takes 6 of them to make a full turn.
Final Answer:
1. Measure of angles:
72°
It takes
5 angles of
72° to make a full turn.
2. Measure of angles:
36°
It takes
10 angles of
36° to make a full turn.
3. Measure of angles:
90°
It takes
4 angles of
90° to make a full turn.
4. Measure of angles:
180°
It takes
2 angles of
180° to make a full turn.
5. Measure of angles:
40°
It takes
9 angles of
40° to make a full turn.
6. Measure of angles:
45°
It takes
8 angles of
45° to make a full turn.
7. Measure of angles:
120°
It takes
3 angles of
120° to make a full turn.
8. Measure of angles:
60°
It takes
6 angles of
60° to make a full turn.
Parent Tip: Review the logic above to help your child master the concept of 4th grade math angles worksheet.
