Acute / Obtuse Isosceles Triangles

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Math › Acute / Obtuse Isosceles Triangles

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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:

Thus for the vertex angle and for the base angle.

The sum of the vertex and one base angle is .

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:

Thus for the vertex angle and for the base angle.

The sum of the vertex and one base angle is .

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 .

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 .

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 .

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 .

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 .

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?