# PSAT Math : Geometry

## Example Questions

### Example Question #5 : Hexagons

Note: Figure NOT drawn to scale.

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

Insufficient information is given to answer the problem.

Explanation:

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  ?

Explanation:

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

Explanation:

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:

210

180

170

190

200

190

Explanation:

### 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?

Explanation:

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?

150 degrees

120 degrees

105 degrees

72 degrees

90 degrees

120 degrees

Explanation:

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 .

Explanation:

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 .

Explanation:

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?

This hexagon cannot exist.

Explanation:

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?