Answer:
The measure of angle ACE = 40°
Step-by-step explanation:
* Lets explain some information
- A secant is a line that intersects a circle in exactly two points.
- When two secants, intersect each other outside a circle,
then the measure of the angle formed is one-half the positive
difference of the measures of the intercepted arcs.
* Now the two secants AB and ED intersect each other outside
the circle at point C and formed angle ACE
- Angle ACE intercepted by two minor arcs. arc BD and arc AE
- The measure of angle ACE is one-half the positive difference
of the arcs BD and AE
* Lets calculate the measures of the arcs to find the measure
of the angle
∵ The measure of minor arc AB = 112°
∵ The measure of minor arc BD = 28°
∵ The measure of minor arc DE = 112°
∵ The measure of the circle is 360°
∴ The measure of arc AE = 360 - (112 + 28 + 112) = 360 - 252 = 108°
* Now we can find the measure of angle ACE
∵ m∠ACE = (1/2)(measure of arc AE - measure of arc BD)
∴ m∠ACE = (1/2)(108 - 28) = (1/2)(80) = 40°
* The measure of angle ACE = 40°
