∠ACE is formed by two secants intersecting outside of a circle. If minor arc BD = 25°, minor arc AB = 115°, and minor arc DE = 115°, what is the measure of ∠ACE? A) 12.5° B) 40° C) 45° D) 52.5°

Accepted Solution

Answer:The measure of angle ACE = 40° ⇒ answer (B)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 = 115°∵ The measure of minor arc BD = 25°∵ The measure of minor arc DE = 115°∵ The measure of the circle is 360°∴ The measure of arc AE = 360 - (115 + 25 + 115) = 360 - 255 = 105°* 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)(105 - 25) = (1/2)(80) = 40°* The measure of angle ACE = 40°