How to find an angle in an acute / obtuse triangle

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GRE Quantitative Reasoning › How to find an angle in an acute / obtuse triangle

Questions 1 - 3
1

Gre14

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

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

2

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

10

15

20

25

30

Explanation

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

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

15_x_ + 30 = 180

15_x_ = 150

x = 10

3

Varsity

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

Quantity A Quantity B

angle C the sum of angle A and angle B

Quantity A is greater

Quantity B is greater

Quantity A and B are equal

The relationship cannot be determined from the information given.

Explanation

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.

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