# Basic Geometry : Plane Geometry

## Example Questions

### Example Question #41 : Lines

If lines A and B are parallel, what is the measurement for ?

Explanation:

When parallel lines are cut by a transversal, vertical angles are congruent.

The given angle and  are vertical angles.

must also have the same mesaurement as the given angle.

### Example Question #42 : Lines

If lines A and B are parallel, what is the measurement of angle 5?

Explanation:

Notice that  and  are supplementary, meaning their angle measurements add up to .

Now, notice that  and the given angle are corresponding angles, meaning that their measurements are the same.

Thus,

### Example Question #43 : Lines

If lines D and E are parallel, what is the measure of ?

Explanation:

The given angle and  are supplementary, meaning their angle measurements add up to .

Subtract 127 from both sides to find the measurement of angle seven.

### Example Question #44 : Lines

If lines D and E are parallel, what is the measure of ?

Explanation:

The given angle and  are interior consecutive angles, meaning they add up to .

Subtract 127 from both sides to find the measurement of angle eight.

### Example Question #45 : Lines

If lines D and E are parallel, what is the measure of ?

Explanation:

The given angle and  are corresponding angles. Corresponding angles share the same value.

must then be equal to the given value.

Therefore,

### Example Question #46 : Lines

If lines D and E are parallel, what is the measure of ?

The measure of  cannot be determined.

Explanation:

The given angle and  are vertical angles. Vertical angles are congruent.

must have the same measure as the given angle.

Therefore,

### Example Question #47 : Lines

If lines D and E are parallel, what is the measure of ?

Explanation:

The given angle and  are alternative interior angles. Alternate interior angles are congruent.

must have the same measure as the given angle.

### Example Question #48 : Lines

If lines D and E are parallel, what is the measure of ?

Explanation:

The given angle and  are supplementary, meaning that their values must add up to .

Subtract 127 from both sides to find the measurement of angle twelve.

### Example Question #49 : Lines

An scalene triangle has has interior angles of , and . How many obtuse interior angles does the triangle have?

There is not enough information given.

Explanation:

In order to answer the question, we have to figure out what each of the angles is, and then see if any of them are obtuse. The way we do this is to solve for the value of .

To solve for , we must know that the interior angles of a triangle add up to equal .

Therefore, we can set up the following equation and solve for :

We can then plug in this value to find the three angles:

Because an obtuse angle is larger than , none of the angles of this triangle are obtuse.

### Example Question #50 : Lines

An obtuse angle is an angle that:

is between 0 and 45 degrees

is equal to 180 degrees

is between 0 and 90 degrees

is between 90 and 180 degrees

is equal to 90 degrees