Mason cuts a giant circular cookie into 5 equal pieces. Which statements are true about the angle measures of the pieces? Select all that apply.

Question

(1 point)
Responses

12
of the cookie has a total angle measure of 160°

1 2 of the cookie has a total angle measure of 160°

4 pieces have a total angle measure of 225°

4 pieces have a total angle measure of 225°

Each piece has an angle measure of 72°

Each piece has an angle measure of 72°

2 pieces have a total angle measure of 120°

2 pieces have a total angle measure of 120°

One 90° angle can fit into 2 pieces of cookie

Answer 1

To determine which statements about the angle measures of the pieces are true, let’s first analyze the situation:

1. A full circle has a total angle measure of 360°.
2. Mason cuts the cookie into 5 equal pieces, so each piece has an angle measure of \( \frac{360°}{5} = 72° \).

Now, let's evaluate each statement:

1. 12 of the cookie has a total angle measure of 160° - False. The total angle measure is referring to a fraction of the circle, not applicable here.

2. 1 2 of the cookie has a total angle measure of 160° - False. This seems to have a typo; it should probably say "1/2", which would be 180°, not 160°.

3. 4 pieces have a total angle measure of 225° - False. If each piece is 72°, then 4 pieces would have \( 4 \times 72° = 288° \).

4. Each piece has an angle measure of 72° - True. This is correct based on our calculation.

5. 2 pieces have a total angle measure of 120° - False. Two pieces would have \( 2 \times 72° = 144° \).

6. One 90° angle can fit into 2 pieces of cookie - True. Since 2 pieces measure 144°, a 90° angle can fit into that total.

Therefore, the true statements are:

• Each piece has an angle measure of 72°.
• One 90° angle can fit into 2 pieces of cookie.