### All PSAT Math Resources

## Example Questions

### Example Question #5 : Hexagons

Note: Figure NOT drawn to scale.

The perimeter of the above hexagon is 888. Also, . Evaluate .

**Possible Answers:**

Insufficient information is given to answer the problem.

**Correct answer:**

The perimeter of the figure can be expressed in terms of the variables by adding:

Simplify and set :

Along with , we now have a system of equations to solve for by adding:

### Example Question #6 : Hexagons

Note: Figure NOT drawn to scale.

The perimeter of the above figure is 132. What is ?

**Possible Answers:**

**Correct answer:**

The perimeter of the figure can be expressed in terms of the variables by adding:

Simplify and set :

### Example Question #7 : Hexagons

Note: Figure NOT drawn to scale.

The perimeter of the above figure is 600. The ratio of to is . Evaluate .

**Possible Answers:**

**Correct answer:**

The perimeter of the figure can be expressed in terms of the variables by adding:

Simplify and set :

Since the ratio of to is equivalent to - or

,

then

and we can substitute as follows:

### Example Question #1 : How To Find An Angle In A Hexagon

**Possible Answers:**

210

180

170

190

200

### Example Question #2 : How To Find An Angle In A Hexagon

If a triangle has 180 degrees, what is the sum of the interior angles of a regular octagon?

**Possible Answers:**

**Correct answer:**

The sum of the interior angles of a polygon is given by where = number of sides of the polygon. An octagon has 8 sides, so the formula becomes

### Example Question #3 : How To Find An Angle In A Hexagon

In a rectangular hexagon, what is the meaure of each interior angle?

**Possible Answers:**

150 degrees

120 degrees

105 degrees

72 degrees

90 degrees

**Correct answer:**

120 degrees

The sum of the interior angles of a hexagon must equal 720 degrees. Because the hexagon is regular, all of the interior angles will have the same measure. A hexagon has six sides and six interior angles. Therefore, each angle measures.

### Example Question #4 : How To Find An Angle In A Hexagon

Note:Figure NOT drawn to scale.

Refer to the above figure. Evaluate .

**Possible Answers:**

**Correct answer:**

The sum of the degree measures of the angles of a (six-sided) hexagon, is

We can solve for in the equation

### Example Question #5 : How To Find An Angle In A Hexagon

Note: Figure NOT drawn to scale.

Refer to the above figure. Evaluate .

**Possible Answers:**

**Correct answer:**

The sum of the degree measures of the angles of a (six-sided) hexagon, is

We can solve for in the equation

### Example Question #6 : How To Find An Angle In A Hexagon

Three angles of a hexagon measure . The other three angles are congruent to one another. What is the measure of each of the latter three angles?

**Possible Answers:**

This hexagon cannot exist.

**Correct answer:**

The sum of the degree measures of the angles of a (six-sided) hexagon, is

Let be the common measure of the three congruent angles in question. We can solve for in the equation

### Example Question #7 : How To Find An Angle In A Hexagon

What is the measurement of one of the interior angles of a regular hexagon?

**Possible Answers:**

**Correct answer:**

To find the sum of the interior angles of any regular polygon, use the formula , where represents the number of sides of the regular polygon.

The sum of the interior angles of a regular hexagon is 720 degrees. To find the measurement of one angle, divide by the number of interior angles (or sides):

The measurement of one angle in a regular hexagon is 120 degrees.

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