All SAT Math Resources
Example Questions
Example Question #11 : How To Find An Angle In A Polygon
To the nearest whole degree, give the measure of each interior angle of a regular polygon with 17 sides.
The measure of each interior angle of an -sided polygon can be calculated using the formula
Setting :
The correct choice is therefore .
Example Question #371 : Sat Mathematics
Each interior angle of a regular polygon has measure . How many sides does the polygon have?
The easiest way to work this is arguably to examine the exterior angles, each of which forms a linear pair with an interior angle. If an interior angle measures , then each exterior angle, which is supplementary to an interior angle, measures
The measures of the exterior angles of a polygon, one per vertex, total ; in a regular polygon, they are congruent, so if there are
such angles, each measures
. Since the number of vertices is equal to the number of sides, if we set this equal to
and solve for
, we will find the number of sides.
Multiply both sides by :
The polygon has 72 vertices and, thus, 72 sides.
Example Question #1 : How To Find An Angle In A Polygon
A regular polygon has a measure of for each of its internal angles. How many sides does it have?
To determine the measure of the angles of a regular polygon use:
Angle = (n – 2) x 180° / n
Thus, (n – 2) x 180° / n = 140°
180° n - 360° = 140° n
40° n = 360°
n = 360° / 40° = 9
Example Question #1 : How To Find An Angle In A Polygon
A regular seven sided polygon has a side length of 14”. What is the measurement of one of the interior angles of the polygon?
257.14 degrees
252 degrees
180 degrees
154.28 degrees
128.57 degrees
128.57 degrees
The formula for of interior angles based on a polygon with a number of side n is:
Each Interior Angle = (n-2)*180/n
= (7-2)*180/7 = 128.57 degrees
Certified Tutor
Certified Tutor
All SAT Math Resources
