Question

In circle D, DE = 15 and the length of EF = 12π. Find m angle EDF. Answer: m angle EDF = ? (attempt 1 out of 3, problem 1 out of max 6).

Answer 1

To find the measure of angle EDF in circle D, we can use the length of arc EF and the circumference of the circle. By setting up a proportion, we can find that angle EDF is equal to 144°.

Step-by-step explanation:

To find the measure of angle EDF, we first need to find the length of arc DF. We can use the formula for the circumference of a circle, C=2πr, where r is the radius of the circle. In this case, the radius is DE, so C=2π(15)=30π.

The length of arc EF is given as 12π. To find the measure of angle EDF, we can set up a proportion:

arc EF / circumference = angle EDF / 360°

12π / 30π = angle EDF / 360°

Simplifying, we get:

12/30 = angle EDF/360°

0.4 = angle EDF/360°

To solve for angle EDF, we can multiply both sides by 360°:

0.4 * 360° = angle EDF

angle EDF = 144°