### All GRE Math Resources

## Example Questions

### Example Question #1 : Pentagons

In a five-sided polygon, one angle measures . What are the possible measurements of the other angles?

**Possible Answers:**

**Correct answer:**

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

In this case:

The sum of the interior angles will be 540. Go through each answer choice and see which one adds up to 540 (including the original angle given in the problem).

The only one that does is 120, 115, 95, 105 and the original angle of 105.

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

In a particular heptagon (a seven-sided polygon) the sum of four equal interior angles, each equal to degrees, is equivalent to the sum of the remaining three interior angles.

Quantity A:

Quantity B:

**Possible Answers:**

Quantity B is greater

Quantity A is greater.

The relationship cannot be determined.

The two quantities are equal.

**Correct answer:**

Quantity A is greater.

The sum of interior angles in a heptagon is degrees. Note that to find the sum of interior angles of any polygon, it is given by the formula:

degrees, where is the number of sides of the polygon.

Three interior angles (call them ) are unknown, but we are told that the sum of them is equal to the sum of four other equivalent angles (which we'll designate ):

Further more, all of these angles must sum up to degrees:

We may not be able to find , , or , indvidually, but the problem does not call for that, and we need only use their relation to , as stated in the first equation with them. Utilizing this in the second, we find:

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

What is the value of in the figure above?

**Possible Answers:**

**Correct answer:**

Always begin working through problems like this by filling in all available information. We know that we can fill in two of the angles, giving us the following figure:

Now, we know that for any polygon, the total number of degrees in the figure can be calculated by the equation:

, where is the number of sides.

Thus, for our figure, we have:

Based on this, we know:

Simplifying, we get:

Solving for , we get:

or

### Example Question #51 : Geometry

Quantity A: The measure of the largest angle in the figure above.

Quantity B:

Which of the following is true?

**Possible Answers:**

The two quantities are equal.

Quantity B is larger.

Quantity A is larger.

The relationship cannot be determined.

**Correct answer:**

Quantity A is larger.

To begin, recall that the total degrees in any figure can be calculated by:

, where represents the total number of sides. Thus, we know for our figure that:

Now, based on our figure, we can make the equation:

Simplifying, we get:

or

This means that is . Quantity A is larger.

### Example Question #1 : Triangles

What is the perimeter of an isosceles triangle given that the sides 5 units long and half of the base measures to 4 units?

**Possible Answers:**

**Correct answer:**18

The base of the triangle is 4 + 4 = 8 so the total perimeter is 5 + 5 + 8 = 18.

### Example Question #1 : Triangles

An acute Isosceles triangle has two sides with length and one side length . The length of side ft. If the length of half the length of side , what is the perimeter of the triangle?

**Possible Answers:**

foot

foot

inches

foot

inches

**Correct answer:**

inches

This Isosceles triangle has two sides with a length of foot and one side length that is half of the length of the two equivalent sides.

To find the missing side, double the value of side 's denominator:

. Thus, half of .

Therefore, this triangle has two sides with lengths of and one side length of .

To find the perimeter, apply the formula:

foot inches

### Example Question #53 : Geometry

An acute Isosceles triangle has two sides with length and one side length . The length of side . If the length of half the length of side , what is the perimeter of the triangle?

**Possible Answers:**

**Correct answer:**

To solve this problem apply the formula: .

However, first calculate the length of the missing side by: .

Thus, the solution is:

### Example Question #54 : Geometry

Find the perimeter of the acute Isosceles triangle shown above.

**Possible Answers:**

**Correct answer:**

To solve this problem apply the formula: .

However, first calculate the length of the missing side by:

### Example Question #55 : Geometry

An obtuse Isosceles triangle has two sides with length and one side length . The length of side ft. If the length of half the length of side , what is the perimeter of the triangle?

**Possible Answers:**

ft

ft

ft

ft

**Correct answer:**

ft

By definition, an Isosceles triangle must have two equivalent side lengths. Since we are told that ft and that the sides with length are half the length of side , find the length of by: and half of . Thus, both of sides with length must equal ft.

Now, apply the formula: .

Then, simplify the fraction/convert to mixed number fraction:

### Example Question #56 : Geometry

Find the perimeter of the acute Isosceles triangle shown above.

**Possible Answers:**

**Correct answer:**

In order to solve this problem, first find the length of the missing sides. Then apply the formula:

Each of the missing sides equal:

Then apply the perimeter formula: