# High School Math : How to find an angle in an acute / obtuse triangle

## Example Questions

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### Example Question #1 : Acute / Obtuse Triangles

Solve for . (Not drawn to scale).

Explanation:

The angles of a triangle must add to 180o. In the triangle to the right, we know one angle and can find another using supplementary angles.

Now we only need to solve for .

### Example Question #1 : Acute / Obtuse Triangles

If  and , what is the measure of ?

Not enough information to solve

Explanation:

All of the interior angles of a triangle add up to .

If  and , then

Therefore,

Now,  will equal because  and  form a straight line.  Therefore,

Also, by definition, the angle of an exterior angle of a triangle is equal to the measure of the two interior angles opposite of it .

### Example Question #1 : Acute / Obtuse Triangles

Two interior angles in an obtuse triangle measure  and . What is the measurement of the third angle.

Explanation:

Interior angles of a triangle always add up to 180 degrees.

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

In a given triangle, the angles are in a ratio of 1:3:5.  What size is the middle angle?

Explanation:

Since the sum of the angles of a triangle is , and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be , then the following expression could be written:

If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.

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

Triangle ABC has angle measures as follows:

What is ?

19

79

90

44

57

57

Explanation:

The sum of the measures of the angles of a triangle is 180.

Thus we set up the equation

After combining like terms and cancelling, we have

Thus

### Example Question #2 : How To Find An Angle In An Acute / Obtuse Triangle

The base angle of an isosceles triangle is five more than twice the vertex angle.  What is the base angle?

Explanation:

Every triangle has 180 degrees.  An isosceles triangle has one vertex angle and two congruent base angles.

Let  = the vertex angle and  = the base angle

So the equation to solve becomes

Thus the vertex angle is 34 and the base angles are 73.

### Example Question #3 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

The base angle of an isosceles triangle is 15 less than three times the vertex angle.  What is the vertex angle?

Explanation:

Every triangle contains 180 degrees.  An isosceles triangle has one vertex angle and two congruent base angles.

Let  = vertex angle and  = base angle

So the equation to solve becomes .

### Example Question #161 : Sat Mathematics

The base angle of an isosceles triangle is ten less than twice the vertex angle.  What is the vertex angle?

Explanation:

Every triangle has 180 degrees.  An isosceles triangle has one vertex angle and two congruent base angles.

Let  = vertex angle and  = base angle

So the equation to solve becomes

So the vertex angle is 40 and the base angles is 70

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

The base angle of an isosceles triangle is 10 more than twice the vertex angle.  What is the vertex angle?

Explanation:

Every triangle has 180 degrees.  An isosceles triangle has one vertex angle and two congruent base angles.

Let = the vertex angle and  = the base angle

So the equation to solve becomes

The vertex angle is 32 degrees and the base angle is 74 degrees

### Example Question #3 : Acute / Obtuse Isosceles Triangles

In an isosceles triangle, the vertex angle is 15 less than the base angle.  What is the base angle?