### All GED Math Resources

## Example Questions

### Example Question #21 : Other Shapes

What is the measure of each angle of a regular octagon?

**Possible Answers:**

**Correct answer:**

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 #2 : Angles

Give the measure of each interior angle of a regular 72-sided polygon.

**Possible Answers:**

**Correct answer:**

A regular polygon with sides has interior angles of measure each. Substitute 72 for .

### Example Question #3 : Angles

Refer to the above diagram.

Which of these is a valid alternative name for ?

**Possible Answers:**

**Correct answer:**

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 #1 : Angles

Note: Figure NOT drawn to scale.

The above hexagon is regular. What is ?

**Possible Answers:**

**Correct answer:**

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 #5 : Angles

The above octagon is regular. What is ?

**Possible Answers:**

**Correct answer:**

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 #6 : Angles

Note: Figure NOT drawn to scale.

Refer to the above figure. is equilateral and Pentagon is regular.

Evaluate .

**Possible Answers:**

**Correct answer:**

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 #1 : Angles

Refer to the above figure, which shows Square and regular Pentagon .

Evaluate .

**Possible Answers:**

**Correct answer:**

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 #2 : Angles

Refer to the above figure. is equilateral, and Quadrilateral is a square.

Evaluate .

**Possible Answers:**

**Correct answer:**

By angle addition,

.

, as an angle of an equilateral triangle, has measure .

, as an angle of a square, has measure .

Therefore,

.

### Example Question #9 : Angles

Give the number of sides of a regular polygon whose interior angles have measure .

**Possible Answers:**

**Correct answer:**

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 #1 : Angles

Three consecutive even angles add up to . What must be the value of the second largest angle?

**Possible Answers:**

**Correct answer:**

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:

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