GRE Math : How to find an angle in an acute / obtuse triangle

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : Acute / Obtuse Triangles

The three angles in a triangle measure 3x, 4x + 10, and 8x + 20. What is x?

Possible Answers:






Correct answer:



We know the angles in a triangle must add up to 180, so we can solve for x

3x + 4x + 10 + 8x + 20 = 180

15x + 30 = 180

15x = 150

x = 10

Example Question #2 : Acute / Obtuse Triangles


In triangle ABC, AB=6, AC=3, and BC=4. 

Quantity A                               Quantity B

 angle C                   the sum of angle A and angle B 

Possible Answers:

Quantity B is greater

Quantity A and B are equal

The relationship cannot be determined from the information given.

Quantity A is greater

Correct answer:

Quantity A is greater


The given triangle is obtuse. Thus, angle  is greater than 90 degrees. A triangle has a sum of 180 degrees, so angle  + angle  + angle  = 180. Since angle C is greater than 90 then angle  + angle  must be less than 90 and it follows that Quantity A is greater. 

Example Question #3 : Acute / Obtuse Triangles


In the figure above, what is the value of angle x?

Possible Answers:

Correct answer:


To find the top inner angle, recognize that a straight line contains 180o; thus we can subtract 180 – 115 = 65o. Since we are given the other interior angle of 30 degrees, we can add the two we know: 65 + 30 = 95o.

180 - 95 = 85

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