All ISEE Upper Level Math Resources
Example Questions
Example Question #2 : How To Find An Angle
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
All ISEE Upper Level Math Resources
