All GED Math Resources
Example Questions
Example Question #21 : Other Shapes
What is the measure of each angle of a regular octagon?
The sum of the degree measures of the angles of a polygon with sides is . Since an octagon has eight sides, substitute to get:
Each angle of a regular polygon has equal measure, so divide this by 8 to get the measure of one angle:
, the degree measure of one angle.
Example Question #421 : 2 Dimensional Geometry
Give the measure of each interior angle of a regular 72-sided polygon.
A regular polygon with sides has interior angles of measure each. Substitute 72 for .
Example Question #1 : Angles
Refer to the above diagram.
Which of these is a valid alternative name for ?
When naming an angle after three points, the middle letter must be its vertex, or the point at which its sides meet - this is . The other two letters must refer to points on its two sides. Therefore, includes on one side, making one of its sides , and on the other, making the other side .
An alternative name for this angle must be one of two things:
It can be named only after its vertex - that is, - but only if there is no ambiguity as to which angle is being named. Since more than one angle in the diagram has vertex , is not a correct choice.
It can be named after three points. Again, the middle letter must be vertex , so we can throw out and .
The only possible choice is .
Example Question #31 : Other Shapes
Note: Figure NOT drawn to scale.
The above hexagon is regular. What is ?
Two of the angles of the quadrilateral formed are angles of a regular hexagon, so each measures
.
The four angles of the quadrilateral are . Their sum is , so we can set up an equation and solve for :
Example Question #3 : Angles
The above octagon is regular. What is ?
Three of the angles of the pentagon formed are angles of a regular octagon, so each measures
.
The five angles of the pentagon are . Their sum is , so we can set up an equation and solve for :
Example Question #2 : Angles
Note: Figure NOT drawn to scale.
Refer to the above figure. is equilateral and Pentagon is regular.
Evaluate .
First, we find .
By angle addition,
.
is an angle of a regular pentagon and has measure .
, as an angle of an equilateral triangle, has measure .
is equilateral, so ; Pentagon is regular, so . Therefore, , and by the Isosceles Triangle Theorem, .
The degree measures of three angles of a triangle total , so:
Example Question #423 : 2 Dimensional Geometry
Refer to the above figure, which shows Square and regular Pentagon .
Evaluate .
By angle addition,
.
is an angle of a regular pentagon and has measure .
is one of two acute angles of isosceles right triangle , so .
Example Question #32 : Other Shapes
Refer to the above figure. is equilateral, and Quadrilateral is a square.
Evaluate .
By angle addition,
.
, as an angle of an equilateral triangle, has measure .
, as an angle of a square, has measure .
Therefore,
.
Example Question #1391 : Ged Math
Give the number of sides of a regular polygon whose interior angles have measure .
The easiest way to solve this is to look at the exterior angles, each of which have measure . Since each exterior angle of a regular polygon with sides is , we solve for in the following equation:
The polygon has 36 sides.
Example Question #3 : Angles
Three consecutive even angles add up to . What must be the value of the second largest angle?
Let be an even angle. The next consecutive even values are .
Set up an equation such that all angles added equal to 180.
Divide by three on both sides.
The second largest angle is .
Substitute the value of in to the expression.
The answer is: