# Intermediate Geometry : How to find an angle in an acute / obtuse triangle

## Example Questions

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### Example Question #21 : How To Find An Angle In An Acute / Obtuse Triangle

Two of the exterior angles of a triangle, taken at different vertices, measure and . Is the triangle acute, right, or obtuse?

Acute

Obtuse

Right

Right

Explanation:

At a given vertex, an exterior angle and an interior angle of a triangle form a linear pair, making them supplementary - that is, their measures total . The measures of two interior angles can be calculated by subtracting the exterior angle measures from :  The triangle has two interior angles of measures and . The sum of these measures is , thereby making them complementary. A triangle with two complementary acute angles is a right triangle.

### Example Question #22 : How To Find An Angle In An Acute / Obtuse Triangle

True or false: It is possible for a triangle to have angles of measure  , and .

True

False

True

Explanation:

The sum of the measures of the angles of a triangle is . The sum of the three given angle measures is .

This makes the triangle possible.

### Example Question #23 : How To Find An Angle In An Acute / Obtuse Triangle

True or false: It is possible for a triangle to have three interior angles, each of whose measures are .

True

False

False

Explanation:

A triangle with three congruent angles is an equiangular - and equilateral - triangle; such an angle must have three angles that measure ### Example Question #24 : How To Find An Angle In An Acute / Obtuse Triangle

Given: with perimeter 40; True or false: True

False

True

Explanation:

The perimeter of is the sum of the lengths of its sides - that is, The perimeter is 40, so set , and solve for :   Subtract 26 from both sides:   , so by the Isosceles Triangle Theorem, their opposite angles are congruent - that is, .

### Example Question #51 : Acute / Obtuse Triangles is an equilateral triangle; is the midpoint of ; the segment is constructed.

True or false: .

True

False

False

Explanation:

The referenced triangle is below: In an equilateral triangle, the median from - the segment from to , the midpoint of the opposite side - is also the bisector of the angle , so Each interior angle of an equilateral triangle, including , measures , so substitute and evaluate: .

### Example Question #26 : How To Find An Angle In An Acute / Obtuse Triangle is an equilateral triangle. Locate a point along and construct  Evaluate .      Explanation:

The referenced figure is below. Note that , as is the case with all of the interior angles of an equilateral triangle. The interior angles of an equilateral triangle each measure . An exterior angle of a triangle has as its degree measure the sum of its remote interior angles; specifically, Substitute the known angle measures, and solve:   1 3 Next → 