Intermediate Geometry : How to find an angle in an acute / obtuse isosceles triangle

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

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

An isoceles triangle has a vertex angle that is twenty more than twice the base angle.  What is the difference between the vertex and base angles?

Possible Answers:

Correct answer:

Explanation:

A triangle has degrees.  An isoceles triangle has one vertex angle and two congruent base angles.

Let = the base angle and  = vertex angle

So the equation to solve becomes 

or

 

so the base angle is and the vertex angle is and the difference is .

Example Question #2 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

An ssosceles triangle has interior angles of  degrees and  degrees. Find the missing angle. 

Possible Answers:

 

 

 

 

Correct answer:

 

Explanation:

Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of  degrees. 

Thus, the solution is:





Example Question #3 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

The largest angle in an obtuse isosceles triangle is  degrees. Find the measurement of one of the two equivalent interior angles. 

Possible Answers:

 

 

 

 

Correct answer:

 

Explanation:

Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of  degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles.  

Thus, the solution is:



Example Question #4 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

The two equivalent interior angles of an obtuse isosceles triangle each have a measurement of  degrees. Find the measurement of the obtuse angle. 

Possible Answers:

 

 

 

 

Correct answer:

 

Explanation:

Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of  degrees.

Thus, the solution is:



Example Question #5 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

In an obtuse isosceles triangle the angle measurements are, , and . Find the measurement of one of the acute angles. 

Possible Answers:

 

 

 

 

 

Correct answer:

 

Explanation:

Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of  degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles. 

The solution is:



However,  degrees is the measurement of both of the acute angles combined.

Each individual angle is .

Example Question #6 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

In an acute isosceles triangle the two equivalent interior angles each have a measurement of  degrees. Find the missing angle. 

Possible Answers:

 

 

 

 

Correct answer:

 

Explanation:

Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of  degrees. Since this is an acute isosceles triangle, all of the interior angles must be acute angles.

The solution is:



 

Example Question #7 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

In an acute isosceles triangle the two equivalent interior angles are each  degrees. Find the missing angle. 

Possible Answers:

 

 

 

 

Correct answer:

 

Explanation:

Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of  degrees. Since this is an acute isosceles triangle, all of the interior angles must be acute angles.

The solution is:



Example Question #8 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

The largest angle in an obtuse isosceles triangle is  degrees. Find the measurement of one of the equivalent interior angles. 

Possible Answers:

 

 

 

 

 

Correct answer:

 

Explanation:

Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of  degrees. Since this is an obtuse Isosceles triangle, the two missing angles must be acute angles.  

Thus, the solution is:



Example Question #9 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

In an obtuse isosceles triangle the largest angle is  degrees. Find the measurement of one of the acute angles. 

Possible Answers:

 

 

 

 

 

Correct answer:

 

Explanation:

Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of  degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles. 

The solution is:



Example Question #10 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

In an acute isosceles triangle the measurement of the non-equivalent interior angle is  degrees. Find the measurement of one of the equivalent interior angles. 

Possible Answers:

 

 

 

Correct answer:

 

Explanation:

Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of  degrees. Since this is an acute isosceles triangle, all of the interior angles must be acute angles.

The solution is:



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