### All GED Math Resources

## Example Questions

### Example Question #1 : Opposite And Corresponding Angles

Refer to the above diagram.

Which of the following is a valid alternative name for ?

**Possible Answers:**

**Correct answer:**

The name of a ray includes two letters, so can be eliminated.

The first letter must be the endpoint. Since is a name of the ray, the endpoint is , and any alternative name for the ray must begin with . This leaves only .

### Example Question #2 : Opposite And Corresponding Angles

Refer to the above diagram.

; ; .

What is ?

**Possible Answers:**

**Correct answer:**

and are two acute angles of a right triangle and are therefore complementary - that is,

, so

and , being alternate interior angles formed by transversal across parallel lines, are congruent, so .

We now look at , whose interior angles must have degree measures totaling , so

### Example Question #3 : Opposite And Corresponding Angles

Refer to the above diagram.

Which of the following facts does not, by itself, prove that ?

**Possible Answers:**

and are supplementary angles

bisects

is a right angle

**Correct answer:**

bisects

From the Parallel Postulate and its converse, as well as its various resulting theorems, two lines in a plane crossed by a transversal are parallel if any of the following happen:

Both lines are perpendicular to the same third line - this happens if is a right angle, since, from this fact and the fact that is also right, both lines are perpendicular to .

Same-side interior angles are supplementary - this happens if and are supplementary, since they are same-side interior angles with respect to transversal .

Alternate interior angles are congruent - this happens if , since they are alternate interior angles with respect to transversal .

However, the fact that bisects has no bearing on whether is true or not, since it does not relate any two angles formed by a transversal.

" bisects " is the correct choice.

### Example Question #4 : Opposite And Corresponding Angles

In two intersecting lines, the opposite angles are and . What must be the value of ?

**Possible Answers:**

**Correct answer:**

In an intersecting line, vertical angles are equal to each other.

Set up an equation such that both angles are equal.

Solve for . Subtract on both sides.

Add 14 on both sides.

Divide by 7 on both sides.

The answer is:

### Example Question #5 : Opposite And Corresponding Angles

Suppose a pair of opposite angles are measured and . What must the value of ?

**Possible Answers:**

**Correct answer:**

Vertical angles are equal.

Set both angles equal and solve for x.

Subtract on both sides.

Add 8 on both sides.

Divide by 4 on both sides.

The answer is:

### Example Question #6 : Opposite And Corresponding Angles

Suppose two vertical angles in a pair of intersecting lines. What is the value of if one angle is and the other angle is ?

**Possible Answers:**

**Correct answer:**

Vertical angles of intersecting lines must equal to each other.

Set up an equation such that both angle measures are equal.

Add three on both sides.

Divide by three on both sides.

The answer is:

### Example Question #3 : Opposite And Corresponding Angles

Suppose two opposite angles are measured and . What is the value of ?

**Possible Answers:**

**Correct answer:**

Opposite angles equal. Set up an equation such that both angle values are equal.

Add 5 on both sides.

Divide by 5 on both sides.

The answer is:

### Example Question #8 : Opposite And Corresponding Angles

With a pair of intersecting lines, a set of opposite angles are measured and . What must the value of be?

**Possible Answers:**

**Correct answer:**

Opposite angles of two intersecting lines must equal to each other. Set up an equation such that both angle are equal.

Add 9 on both sides.

Subtract on both sides.

This means that equals .

### Example Question #3 : Opposite And Corresponding Angles

In the figure above, . If the measure of and , what is the measure of ?

**Possible Answers:**

**Correct answer:**

Since we have two parallel lines, we know that since they are opposite angle.

We also know that are supplementary because they are consecutive interior angles. Thus, we know that is also supplementary to .

We can then set up the following equation to solve for .

Thus, and .

Now, notice that because they are corresponding angles. Thus, .

### Example Question #551 : 2 Dimensional Geometry

Find the value of .

Assume the two horizontal lines are parallel.

**Possible Answers:**

**Correct answer:**

Start by noticing that the two angles with the values of and are supplementary.

Thus, we can write the following equation and solve for .

Since and are vertical angles, they must also have the same value.

Thus,

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