All ISEE Upper Level Math Resources
Example Questions
Example Question #2041 : Hspt Mathematics
Note: Figure NOT drawn to scale.
Refer to the above diagram. Give the measure of .
The top and bottom angles, being vertical angles - angles which share a vertex and whose union is a pair of lines - have the same measure, so
,
or, simplified,
The right and bottom angles form a linear pair, so their degree measures total 180. That is,
Substitute for :
The left and right angles, being vertical angles, have the same measure, so, since the right angle measures , this is also the measure of the left angle, .
Example Question #41 : Plane Geometry
Figure NOT drawn to scale
The above figure shows Trapezoid , with and tangent to the circle. ; evaluate .
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
Certified Tutor
Certified Tutor