### All GRE Math Resources

## Example Questions

### Example Question #71 : Plane Geometry

The three angles in a triangle measure 3*x*, 4*x* + 10, and 8*x* + 20. What is *x*?

**Possible Answers:**

10

20

30

15

25

**Correct answer:**

10

We know the angles in a triangle must add up to 180, so we can solve for *x*.

3*x* + 4*x* + 10 + 8*x* + 20 = 180

15*x* + 30 = 180

15*x* = 150

*x* = 10

### Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

In triangle ABC, AB=6, AC=3, and BC=4.

Quantity A Quantity B

angle C the sum of angle A and angle B

**Possible Answers:**

Quantity A is greater

Quantity B is greater

Quantity A and B are equal

The relationship cannot be determined from the information given.

**Correct answer:**

Quantity A is greater

The given triangle is obtuse. Thus, angle is greater than 90 degrees. A triangle has a sum of 180 degrees, so angle + angle + angle = 180. Since angle C is greater than 90 then angle + angle must be less than 90 and it follows that Quantity A is greater.

### Example Question #1 : Acute / Obtuse Triangles

In the figure above, what is the value of angle x?

**Possible Answers:**

**Correct answer:**

To find the top inner angle, recognize that a straight line contains 180^{o;} thus we can subtract 180 – 115 = 65^{o}. Since we are given the other interior angle of 30 degrees, we can add the two we know: 65 + 30 = 95^{o}.

180 - 95 = 85