∠ace is formed by two secants intersecting outside of a circle. if minor arc bd = 28°, minor arc ab = 112°, and minor arc de = 112°, what is the measure of ∠ace?

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°

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