What is the value of r if r = 8? 10r = ?
1 answer:
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Answer:
A
Step-by-step explanation:
The Tangent-Secant Exterior Angle Measure Theorem states that if a tangent and a secant or two tangents/secants intersect outside of a circle, then the measure of the angle formed by them is half of the difference of the measures of its intercepted arcs. Basically, what that means here is that equals half of the difference of
and the measure of the unlabeled arc.
First, we need to find the measure of the unlabeled arc, since we can't find without it. We know that the measure of the full arc formed by the circle is
, so the measure of the unlabeled arc must be
by the Arc Addition Postulate.
Now, we can find . Using all of the information known, we can solve for
like this:
Hope this helps!
Given:
A figure of a circle and two secants on the circle from the outside of the circle.
To find:
The measure of angle KLM.
Solution:
According to the intersecting secant theorem, if two secant of a circle intersect each other outside the circle, then the angle formed on the intersection is half of the difference between the intercepted arcs.
Using intersecting secant theorem, we get
Multiply both sides by 2.
Isolate the variable x.
Divide both sides by 7.
Now,
Therefore, the measure of angle KLM is 113 degrees.