# Please explain how to solve the question.?

Relevance
• iceman
Lv 7
3 years ago

Angle AEC = Angle DEB = 4x degrees

Angle Formed by Two Intersecting Chords = 1/2(sum of intercepted arcs), so in this case:

4x = 1/2(120 + 2x)

4x = x + 60

3x = 60

x = 20 degrees

4x = 80 degrees

Angle AED = 1/2(360 - 2*80)

= 1/2(360 - 160)

= 1/2(200)

Angle AED = 100 degrees

Edit: Re: the comment/question: The name of formulas used?

The first formula that was used to find the angles equating to 4x degrees, is driven by a theorem called:

"Angles of intersecting chords" . You can read and review more examples in the link below:

http://www.mathwarehouse.com/geometry/circle/angle...

The second theorem that was use to find angle AED is simply the properties of vertical angles formed by 2 intersecting lines, for more information the please see the link below:

http://www.mathopenref.com/anglesvertical.html

I hope this helps.

• Miriam3 years agoReport

Thank you, did you use a formula to solve this, if so what is it called.