The number of degrees in 2$\frac{2}{3}$ right angles is :

Q: The number of degrees in 2$\frac{2}{3}$ right angles is :

To determine the number of degrees in $2\frac{2}{3}$ right angles, we first need to understand how many degrees are in a single right angle. A right angle is defined as 90 degrees. 1. **Calculate the degrees in $2\frac{2}{3}$ right angles:** - First, convert the mixed number $2\frac{2}{3}$ into an improper fraction: \[ 2\frac{2}{3} = \frac{3 \times 2 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3} \] - Now, multiply the improper fraction by the degrees in one right angle: \[ \frac{8}{3} \times 90 = \frac{8 \times 90}{3} = \frac{720}{3} = 240 \] Therefore, $2\frac{2}{3}$ right angles equal 240 degrees. 2. **Explanation of why Option 3 is correct:** - Option 3 states that the number of degrees is 240, which matches our calculation. Therefore, Option 3 is the correct answer. 3. **Explanation of why the other options are incorrect:** - **Option 1 (210 degrees):** This option is incorrect because when you multiply $\frac{8}{3}$ by 90, you do not get 210. The calculation clearly shows that the result is 240, not 210. - **Option 2 (285 degrees):** This option is incorrect for the same reason. The multiplication of $\frac{8}{3}$ by 90 results in 240, not 285. There is no mathematical basis for arriving at 285 degrees from $2\frac{2}{3}$ right angles. - **Option 4 (330 degrees):** This option is also incorrect. The calculation of $\frac{8}{3} \times 90$ yields 240 degrees, not 330. There is no logical or mathematical justification for 330 degrees in this context. In conclusion, the correct answer is Option 3, which is 240 degrees, as it accurately represents the number of degrees in $2\frac{2}{3}$ right angles based on the calculations provided.

Question

Accepted Answer

To determine the number of degrees in $2\frac{2}{3}$ right angles, we first need to understand how many degrees are in a single right angle. A right angle is defined as 90 degrees.

1. **Calculate the degrees in $2\frac{2}{3}$ right angles:**

- First, convert the mixed number $2\frac{2}{3}$ into an improper fraction:
     $$
     2\frac{2}{3} = \frac{3 \times 2 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}
     $$

- Now, multiply the improper fraction by the degrees in one right angle:
     $$
     \frac{8}{3} \times 90 = \frac{8 \times 90}{3} = \frac{720}{3} = 240
     $$

Therefore, $2\frac{2}{3}$ right angles equal 240 degrees.

2. **Explanation of why Option 3 is correct:**

- Option 3 states that the number of degrees is 240, which matches our calculation. Therefore, Option 3 is the correct answer.

3. **Explanation of why the other options are incorrect:**

- **Option 1 (210 degrees):** This option is incorrect because when you multiply $\frac{8}{3}$ by 90, you do not get 210. The calculation clearly shows that the result is 240, not 210.

- **Option 2 (285 degrees):** This option is incorrect for the same reason. The multiplication of $\frac{8}{3}$ by 90 results in 240, not 285. There is no mathematical basis for arriving at 285 degrees from $2\frac{2}{3}$ right angles.

- **Option 4 (330 degrees):** This option is also incorrect. The calculation of $\frac{8}{3} \times 90$ yields 240 degrees, not 330. There is no logical or mathematical justification for 330 degrees in this context.

In conclusion, the correct answer is Option 3, which is 240 degrees, as it accurately represents the number of degrees in $2\frac{2}{3}$ right angles based on the calculations provided.