Question

∠AED is formed inside a circle by two intersecting chords. If minor arc BD = 70 and minor arc CA = 180, what is the measure of ∠ AED?

Answer 1

I was think vertical angle.

Answer 2

∠AED = 55°

Explanation:

Two chords AB and CD are intersecting each other at E. Minor arc BD is = 70 and minor arc CA is = 180.

We have to find the measurement of ∠AED.

Now we know that ∠CEA =
`(1)/(2)(arcBD+arcCA)=(1)/(2)(70+180)=(1)/(2)(250)=125`

Since ∠CEA + ∠AED = 180° [ Supplementary angles ]

125° + ∠AED = 180

∠AED = 180 - 125 = 55°

Therefore measure of the angle AED = 55° is the answer.