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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #1571 : Plane Geometry

If lines A and B are parallel, what is the measurement for $\angle4$ ?

Possible Answers:

$102^\circ$

$75^\circ$

$89^\circ$

$78^\circ$

Correct answer:

$78^\circ$

Explanation:

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

The given angle and $\angle4$ are vertical angles.

$\angle4$ must also have the same mesaurement as the given angle.

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Example Question #22 : How To Find An Angle Of A Line

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

Possible Answers:

$117^\circ$

$102^\circ$

$78^\circ$

$65^\circ$

Correct answer:

$102^\circ$

Explanation:

Notice that $\angle5$ and $\angle1$ are supplementary, meaning their angle measurements add up to 180 .

$\angle5+\angle1=180^\circ$

Now, notice that $\angle1$ and the given angle are corresponding angles, meaning that their measurements are the same.

Thus,

$\angle5+78^\circ=180^\circ$

$\angle5=102^\circ$

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Example Question #23 : How To Find An Angle Of A Line

If lines D and E are parallel, what is the measure of $\angle7$ ?

Possible Answers:

$87^\circ$

$43^\circ$

$53^\circ$

$127^\circ$

Correct answer:

$53^\circ$

Explanation:

The given angle and $\angle 7$ are supplementary, meaning their angle measurements add up to 180 .

$\angle7+127^\circ=180^\circ$

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

$\angle7=53^\circ$

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Example Question #24 : How To Find An Angle Of A Line

If lines D and E are parallel, what is the measure of $\angle8$ ?

Possible Answers:

$53^\circ$

$127^\circ$

$93^\circ$

$107^\circ$

Correct answer:

$53^\circ$

Explanation:

The given angle and $\angle8$ are interior consecutive angles, meaning they add up to 180 .

$\angle8+127^\circ=180^\circ$

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

$\angle8=53^\circ$

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Example Question #25 : How To Find An Angle Of A Line

If lines D and E are parallel, what is the measure of $\angle9$ ?

Possible Answers:

$165^\circ$

$127^\circ$

$115^\circ$

$97^\circ$

Correct answer:

$127^\circ$

Explanation:

The given angle and $\angle9$ are corresponding angles. Corresponding angles share the same value.

$\angle9$ must then be equal to the given value.

Therefore,

$\angle9=127^\circ$

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Example Question #26 : How To Find An Angle Of A Line

If lines D and E are parallel, what is the measure of $\angle10$ ?

Possible Answers:

$127^\circ$

$156^\circ$

$111^\circ$

The measure of $\angle10$ cannot be determined.

Correct answer:

$127^\circ$

Explanation:

The given angle and $\angle10$ are vertical angles. Vertical angles are congruent.

$\angle10$ must have the same measure as the given angle.

Therefore,

$\angle10=127^\circ$

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Example Question #27 : How To Find An Angle Of A Line

If lines D and E are parallel, what is the measure of $\angle11$ ?

Possible Answers:

$127^\circ$

$57^\circ$

$53^\circ$

$133^\circ$

Correct answer:

$127^\circ$

Explanation:

The given angle and $\angle11$ are alternative interior angles. Alternate interior angles are congruent.

$\angle11$ must have the same measure as the given angle.

$\angle11=127^\circ$

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Example Question #28 : How To Find An Angle Of A Line

If lines D and E are parallel, what is the measure of $\angle12$ ?

Possible Answers:

$63^\circ$

$135^\circ$

$53^\circ$

$91^\circ$

Correct answer:

$53^\circ$

Explanation:

The given angle and $\angle12$ are supplementary, meaning that their values must add up to 180 .

$\angle12+127^\circ=180^\circ$

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

$\angle12=53^\circ$

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Example Question #31 : How To Find An Angle Of A Line

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

Possible Answers:

There is not enough information given.

Correct answer:

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 180^o .

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

x+4x+5x=180

10x=180

$\frac{10x}{10}=\frac{180}{10}$

x=18

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

x=18

4x=4(18)=72

5x=5(18)=90

Because an obtuse angle is larger than 90^o , none of the angles of this triangle are obtuse.

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Example Question #32 : How To Find An Angle Of A Line

An obtuse angle is an angle that:

Possible Answers:

is equal to 180 degrees

is equal to 90 degrees

is between 0 and 90 degrees

is between 90 and 180 degrees

is between 0 and 45 degrees

Correct answer:

is between 90 and 180 degrees

Explanation:

The definition of an obtuse angle is an angle that ranges between 90 and 180 degrees.

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All Basic Geometry Resources

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #1571 : Plane Geometry

Example Question #22 : How To Find An Angle Of A Line

Example Question #23 : How To Find An Angle Of A Line

Example Question #24 : How To Find An Angle Of A Line

Example Question #25 : How To Find An Angle Of A Line

Example Question #26 : How To Find An Angle Of A Line

Example Question #27 : How To Find An Angle Of A Line

Example Question #28 : How To Find An Angle Of A Line

Example Question #31 : How To Find An Angle Of A Line

Example Question #32 : How To Find An Angle Of A Line

All Basic Geometry Resources

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