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

## Example Questions

### Example Question #11 : Triangles

An isosceles triangle has an angle of 110°.  Which of the following angles could also be in the triangle?

20

35

110

90

55

35

Explanation:

An isosceles triangle always has two equal angles. As there cannot be another 110° (the triangle cannot have over 180° total), the other two angles must equal eachother. 180° - 110° = 70°. 70° represents the other two angles, so it needs to be divided in 2 to get the answer of 35°.

### Example Question #11 : Triangles

An isosceles triangle ABC is laid flat on its base.  Given that <B, located in the lower left corner, is 84 degrees, what is the measurement of the top angle, <A?

84
42
20
12
96
Explanation:

Since the triangle is isosceles, and <A is located at the top of the triangle that is on its base, <B and <C are equivalent.  Since <B is 84 degrees, <C is also.  There are 180 degrees in a triangle so 180 - 84 - 84 = 12 degrees.

### Example Question #12 : Triangles

Triangle ABC is isosceles

x and y are positive integers

A

---

x

B

---

y

Quantity B is greater

The relationship cannot be determined

The two quantities are equal

Quantity A is greater

Quantity B is greater

Explanation:

Since we are given expressions for the two congruent angles of the isosceles triangle, we can set the expressions equal to see how x relates to y. We get,

x – 3 = y – 7 --> y = x + 4

Logically, y must be the greater number if it takes x an additional 4 units to reach its value (knowing they are both positive integers).

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

An isosceles triangle has one obtuse angle that is . What is the value of one of the other angles?