### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #41 : Plane Geometry

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

Kevin

Certified Tutor

Certified Tutor

Rutgers University-New Brunswick, Current Undergrad Student, Computer Engineering, General.

### All ISEE Upper Level Math Resources

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