Question

directions: convert each angle measure to degrees.

1. $\frac{3pi}{5}$
2. $-\frac{7pi}{18}$
3. $\frac{10pi}{9}$
4. $\frac{9pi}{5}$
5. $-\frac{11pi}{12}$
6. $\frac{15pi}{4}$

Explanation:

Step1: Recall the conversion formula

To convert radians to degrees, use the formula: Degrees = Radians × $\frac{180^{\circ}}{\pi}$

Step2: Convert $\frac{3\pi}{5}$

For problem 7: Degrees = $\frac{3\pi}{5}$ × $\frac{180^{\circ}}{\pi}$ = $3\times36^{\circ}$ = $108^{\circ}$

Step3: Convert $-\frac{7\pi}{18}$

For problem 8: Degrees = $-\frac{7\pi}{18}$ × $\frac{180^{\circ}}{\pi}$ = $-7\times10^{\circ}$ = $-70^{\circ}$

Step4: Convert $\frac{10\pi}{9}$

For problem 9: Degrees = $\frac{10\pi}{9}$ × $\frac{180^{\circ}}{\pi}$ = $10\times20^{\circ}$ = $200^{\circ}$

Step5: Convert $-\frac{9\pi}{5}$

For problem 10: Degrees = $-\frac{9\pi}{5}$ × $\frac{180^{\circ}}{\pi}$ = $-9\times36^{\circ}$ = $-324^{\circ}$

Step6: Convert $-\frac{11\pi}{12}$

For problem 11: Degrees = $-\frac{11\pi}{12}$ × $\frac{180^{\circ}}{\pi}$ = $-11\times15^{\circ}$ = $-165^{\circ}$

Step7: Convert $\frac{15\pi}{4}$

For problem 12: Degrees = $\frac{15\pi}{4}$ × $\frac{180^{\circ}}{\pi}$ = $15\times45^{\circ}$ = $675^{\circ}$

Answer:

1. $108^{\circ}$
2. $-70^{\circ}$
3. $200^{\circ}$
4. $-324^{\circ}$
5. $-165^{\circ}$
6. $675^{\circ}$