Question

Secants AC and DB intersect at point E inside the circle. Given that the measure of arc CD = 40o, arc AB = 60o, and arc BC = 160 o, which is the measure of AED? A. 80o B. 100o C. 130o D. 160o

Answer 1

C.
`130^(\circ)`

Explanation:

Please find the attachment.

We have been given that secants AC and DB intersect at point E inside the circle. Given that the measure of arc
`CD = 40^o`, arc
`AB = 60^o`, and arc
`BC = 160^o`. We are asked to find the measure of angle AED.

We know that the measure of angle formed by two intersecting secants is half the sum of measure of the arcs by intercepted by the angle and its vertical angle.

`\angle AED=\frac{\widehat{BC}+\widehat{AD}}{2}`

Let us find measure of arc AD by subtracting measure of given arcs from 360 degrees as:

`\widehat{AD}=360^(\circ)-(60^(\circ)+40^(\circ)+160^(\circ))`

`\widehat{AD}=360^(\circ)-(260^(\circ))`

`\widehat{AD}=100^(\circ)`

`\angle AED=(160^(\circ)+100^(\circ))/(2)`

`\angle AED=(260^(\circ))/(2)`

`\angle AED=130^(\circ)`

Therefore, measure of angle AED is 130 degrees and option C is the correct choice.