Question

1. which of the following angles is equivalent to π/6 radians? a. 60 degrees b. 30 degrees c. π/12 radians d. π/3 radians 5. which unit is appropriate for measuring the area of a sector in a circle? a. square centimeters b. centimeters c. meters d. degrees 6. in which type of triangle do the incenter, circumcenter, and centroid all coincide? a. right triangle b. equilateral triangle c. scalene triangle d. isosceles triangle

Explanation:

Step1: Convert radians to degrees

Use the conversion formula $\text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi}$. For $\frac{\pi}{6}$ radians, we have $\frac{\pi}{6}\times\frac{180^{\circ}}{\pi}= 30^{\circ}$.

Step2: Recall area - unit concept

Area is measured in square units. So, the area of a sector of a circle is measured in square centimeters.

Step3: Recall triangle - center properties

In an equilateral triangle, the in - center (center of the inscribed circle), circum - center (center of the circumscribed circle), and centroid (intersection of the medians) coincide.

Answer:

1. B. 30 degrees
2. A. Square centimeters
3. B. Equilateral triangle