I have a circle with a Tangent line, DE, running along it and connecting with another line, FC, which runs through the center of the circle to the other side.I have connected the center of the circle with point E on the edge of the circle with a radius. I have labeled the center of the circle O.
Angle D equals 40 degrees. Angle DEO equals 90 degrees. Angle FOE equals 50 degrees.
What is arc measure EF?
Double post.
See answer by Reiny:
http://www.jiskha.com/display.cgi?id=1244076544
To find the arc measure EF, we can use the relationship between central angles and arc measures. In a circle, the measure of the central angle is equal to the measure of its intercepted arc.
From the given information, we know that angle DEO is a right angle (90 degrees). This means that arc DE is a quarter of the circumference of the circle.
Since angle D is 40 degrees, angle DOF (the central angle of arc DE) will be twice that, or 80 degrees. This means that arc DE is also 80 degrees.
Now, let's look at angle FOE. Since angle FOE is an exterior angle of triangle DEO, it is equal to the sum of the two remote interior angles, which are angles DEO and DOE.
We know that angle DEO is 90 degrees and angle D is 40 degrees. Therefore, angle DOE can be calculated by subtracting 40 degrees from 90 degrees, which gives us 50 degrees.
Since angle FOE is 50 degrees, the intercepted arc EF will also have a measure of 50 degrees.
Therefore, the arc measure EF is 50 degrees.