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 #41 : Triangles

In an obtuse isosceles triangle, the largest interior angle is  degrees. What is 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. 

The solution is:



Example Question #481 : Intermediate Geometry

You are flying a kite at an altitude of 40 feet after having let out 75 feet of string. What is the kite's angle of elevation from where you are holding the spool of string at a height of 4 feet off the ground? Round answer to one decimal place. 

Possible Answers:

Correct answer:

Explanation:

First, we must draw a picture to include all important parts given in the problem. 

Kite1

Once this is determined we can use trigonometry to find the angle of elevation. 

Use the inverse sin on a calculator to solve. 

Example Question #13 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

Two angles in an isosceles triangle are 50 and 80 degrees respectively. What is the measure of the third angle? 

Possible Answers:

Correct answer:

Explanation:

If a triangle is isosceles, two of the angles must be congruent. So the angle must be either 50 degrees or 80 degrees. 

We know that the three angles in all triangles must sum to equal 180 degrees. The only answer choice that is both the same as one of the given angles and results in a sum equal to 180 degrees is the 50 degree angle. 

50+50+80=180. 

Example Question #14 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

An isosceles triangle has one angle measuring . Which of the following are possible values for angles in this triangle?

Possible Answers:

or

or

or

or

or

Correct answer:

or

Explanation:

An isosceles triangle has 2 congruent angles and then a third angle. These angles, as in any triangle, must add to 180.

One possibility is that the 25-degree angle is the "different" one, and the other two are congruent. This could be expressed using the algebraic expression . To find the other two angles, solve for x. First combine like terms:

subtract 25 from both sides

divide both sides by 2

The other possibility is that there are 2 25-degree angles and then some different angle measure. This could be expressed using the algebraic expression . Again, solve for x. First add the 2 25's to get 50:

subtract 50 from both sides

Example Question #481 : Intermediate Geometry

Isosceles

Refer to the above triangle. By what statement does it follow that ?

Possible Answers:

The Converse of the Isosceles Triangle Theorem

The Side-Side-Side Postulate

The Isosceles Triangle Theorem

The Pythagorean Theorem

The Side-Angle-Side Postulate

Correct answer:

The Isosceles Triangle Theorem

Explanation:

We are given that, in , two sides are congruent; specifically, . It is a consequence of the Isosceles Triangle Theorem that the angles opposite the sides are also congruent - that is, .

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