Question

Kite DCFE is inscribed in circle A shown below:

If the measure of arc DEF is 266°, what is the measure of ∠DEF?
Numerical Answers Expected!

Answer 1

check the pictures below.

the arcDEF is the intercepted arc.

Answer 2

133 degrees

Explanation:

Given is a picture of a kite DCFE inscribed in circle A

The vertices of the kite D, C, E and F lie on the circle.

A is the centre.

Arc DEF = 266 degrees

This means the subtended angle of arc DEF at the centre = Angle DAF = 266

By theorem on circles, we have central angle of any arc is twice the angle subtended by the arc on the remaining part of the circumference

Hence

Angle DEF = 1/2 angle DAF

i.e. DEF =
`(266)/(2) =133`

133 degrees