# High School Math : Acute / Obtuse Isosceles Triangles

## Example Questions

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### Example Question #11 : Isosceles Triangles

An isoceles triangle has a base angle that is twice the vertex angle.  What is the sum of the base and vertex angles?

Explanation:

All triangles have degrees.  An isoceles triangle has one vertex angle and two congruent base angles.

Let vertex angle and  base angle.

So the equation to solve becomes:

or

Thus for the vertex angle and for the base angle.

The sum of the vertex and one base angle is .

### Example Question #12 : Isosceles Triangles

An isoceles triangle has a vertex angle that is degrees more than twice the base angle.  What is the vertex angle?

Explanation:

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

Let base angle and vertex angle.

So the equation to solve becomes .

Thus the base angles are and the vertex angle is .

### Example Question #11 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

An isoceles triangle has a base angle that is  degrees less than three times the vertex angle.  What is the product of the vertex angle and the base angle?

Explanation:

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

Let vertex angle and  base angle.

Then the equation to solve becomes:

, or .

Then the vertex angle is , the base angle is , and the product is .

### Example Question #241 : Geometry

In triangle ABC, Angle A = x degrees, Angle B = 2x degrees, and Angle C = 3x+30 degrees. How many degrees is Angle B?

50°

105°

45°

30°

25°

50°

Explanation:

Because the interior angles of a triangle add up to 180°, we can create an equation using the variables given in the problem: x+2x+(3x+30)=180. This simplifies to 6X+30=180. When we subtract 30 from both sides, we get 6x=150. Then, when we divide both sides by 6, we get x=25. Because Angle B=2x degrees, we multiply 25 times 2. Thus, Angle B is equal to 50°. If you got an answer of 25, you may have forgotten to multiply by 2. If you got 105, you may have found Angle C instead of Angle B.

### Example Question #6 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

An isosceles triangle has a base angle that is six more than three times 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  = vertex angle and  = base angle.

Then the equation to solve becomes

or

.

Solving for  gives a vertex angle of 24 degrees and a base angle of 78 degrees.

### Example Question #7 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

The base angle of an isosceles triangle is thirteen more than three times the vertex angle. What is the difference between the vertex angle and the base angle?

Explanation:

Every triangle has . An isosceles triangle has one vertex ange, and two congruent base angles.

Let  be the vertex angle and  be the base angle.

The equation to solve becomes , since the base angle occurs twice.

Now we can solve for the vertex angle.

The difference between the vertex angle and the base angle is .

### Example Question #12 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

An isoceles triangle has a base angle that is five less than twice the vertex angle.  What is the sum of the base and vertex angles?

Explanation:

Each triangle has degrees.

An isoceles triangle has two congruent base angles and one vertex angle.

Let vertex angle and base angle.

Then the equation to solve becomes or .

Add to both sides to get .

Divide both sides by to get vertex angle and base angles, so the sum of the angles is .

### Example Question #13 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

An isoceles triangle has a base angle that is twice the vertex angle.  What is the sum of one base angle and the vertex angle?

Explanation:

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

Let the vertex angle and the base angle

So the equation to solve becomes or and dividing by gives for the vertex angle and for the base angle, so the sum is

### Example Question #1 : How To Find The Length Of The Side Of Of An Acute / Obtuse Isosceles Triangle

A triangle has a perimeter of  inches with one side of length  inches. If the remaining two sides have lengths in a ratio of , what is length of the shortest side of the triangle?