Question

Kite DCFE is inscribed in circle A shown below:

Kite DCFE is inscribed in circle A

If the measure of arc DEF is 266°, what is the measure of ∠DEF? (5 points)

Answer 1

m<DEF = 47°

Explanation:

Given:

m(DEF) = 266°

Required:

m<DEF

Solution:

m<DCF = ½(m(DEF)) (Inscribed angle theorem)

Substitute

m<DCF = ½(266°)

m<DCF = 133°

Opposite angles in an inscribed quadrilateral are supplementary.

Therefore,

m<DEF = 180° - m<DCF

m<DEF = 180° - 133°

m<DEF = 47°