ISEE Upper Level Math : How to find an angle

Study concepts, example questions & explanations for ISEE Upper Level Math

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Example Questions

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Example Question #41 : Plane Geometry

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Figure NOT drawn to scale

The above figure shows Trapezoid , with  and  tangent to the circle. ; evaluate .

Possible Answers:

Correct answer:

Explanation:

By the Same-Side Interior Angle Theorem, since  and  are supplementary - that is, their degree measures total . Therefore, 

 is an inscribed angle, so the arc it intercepts, , has twice its degree measure;

.

The corresponding major arc, , has as its measure 

The measure of an angle formed by two tangents to a circle is equal to half the difference of those of its intercepted arcs:

Again, by the Same-Side Interior Angles Theorem,  and  are supplementary, so

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