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 #71 :Plane Geometry

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

Possible Answers:

10

20

30

15

25

Correct answer:

10

Explanation:

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

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

15x+ 30 = 180

15x= 150

x= 10

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

Varsity

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

Quantity AQuantity B

angle C the sum of angle A and angle B

Possible Answers:

Quantity A is greater

Quantity B is greater

Quantity A and B are equal

The relationship cannot be determined from the information given.

Correct answer:

Quantity A is greater

Explanation:

The given triangle is obtuse. Thus, angleis 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+ anglemust be less than 90 and it follows that Quantity A is greater.

Example Question #1 :Acute / Obtuse Triangles

Gre14

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

Possible Answers:

Correct answer:

Explanation:

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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