Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

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Example Question #11 : Plane Geometry

Angle  measures 

  is the bisector of

  is the bisector of

What is the measure of ?

Possible Answers:

Correct answer:

Explanation:

Angle pic

Let's begin by observing the larger angle.  is cut into two 10-degree angles by . This means that angles  and  equal 10 degrees. Next, we are told that  bisects , which creates two 5-degree angles.   consists of , which is 10 degrees, and , which is 5 degrees. We need to add the two angles together to solve the problem.

Example Question #11 : Plane Geometry

If  , , and , what is the measure, in degrees, of 

Alternate interior angles   

 

Possible Answers:

58

32

148

122

62

Correct answer:

148

Explanation:

The question states that . The alternate interior angle theorem states that if two parallel lines are cut by a transversal, then pairs of alternate interior angles are congruent; therefore, we know the following measure:

The sum of angles of a triangle is equal to 180 degrees. The question states that ; therefore we know the following measure:

Use this information to solve for the missing angle:

The degree measure of a straight line is 180 degrees; therefore, we can write the following equation:

The measure of  is 148 degrees. 

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