In the accompying diagram of circleo, diameter ad,chord AE,ans secantsCAB and CDE are drawn ; m angle BAD=40;and m arch AE=5((m arch ED)
what is the measure of ACE?
To find the measure of ACE, we can use the Triangle Inscribed in a Circle Theorem.
According to the theorem, if a triangle is inscribed in a circle where one side of the triangle is a diameter of the circle, then the angle opposite the diameter is a right angle.
In this case, we have diameter AD, which means angle BAD is a right angle. We're given that m angle BAD = 40 degrees, so we can conclude that m angle CAD is also 40 degrees since they are vertical angles.
Now, we need to find the measure of ACE. Since angle CAD is 40 degrees and angle BAD is a right angle, we can subtract the measure of angle CAD from 90 degrees to find the measure of ACE.
ACE = 90 degrees - 40 degrees = 50 degrees
Therefore, the measure of ACE is 50 degrees.