One of the angles in this triangle is 100 what is the size of each of the other two angles

Isosceles triangle calculator is the best choice if you are looking for a quick solution to your geometry problems. Find out the isosceles triangle area, its perimeter, inradius, circumradius, heights and angles - all in one place. If you want to build a kennel, find out the area of Greek temple isosceles pediment or simply do your maths homework, this tool is here for you. Experiment with the calculator or keep reading to find out more about the isosceles triangle formulas.

An isosceles triangle is a triangle with two sides of equal length, which are called legs. The third side of the triangle is called base. Vertex angle is the angle between the legs and the angles with the base as one of their sides are called the base angles.

Properties of the isosceles triangle:

it has an axis of symmetry along its vertex height
two angles opposite to the legs are equal in length
the isosceles triangle can be acute, right or obtuse, but it depends only on the vertex angle (base angles are always acute)

The equilateral triangle is a special case of a isosceles triangle.

To calculate the isosceles triangle area, you can use many different formulas. The most popular ones are the equations:

Given arm a and base b:

area = (1/4) * b * √( 4 * a² - b² )
Given h height from apex and base b or h2 height from other two vertices and arm a:

area = 0.5 * h * b = 0.5 * h2 * a
Given any angle and arm or base

area = (1/2) * a * b * sin(base_angle) = (1/2) * a² * sin(vertex_angle)

Also, you can check our triangle area calculator to find out other equations, which work for every type of the triangle, not only for the isosceles one.

To calculate the isosceles triangle perimeter, simply add all the triangle sides:
perimeter = a + a + b = 2 * a + b

Isosceles triangle theorem, also known as the base angles theorem, claims that if two sides of a triangle are congruent, then the angles opposite to these sides are congruent.

Also, the converse theorem exists, stating that if two angles of a triangle are congruent, then the sides opposite those angles are congruent.

A golden triangle, which is also called sublime triangle is an isosceles triangle in which the leg is in the golden ratio to the base:

a / b = φ ~ 1.618

The golden triangle has some unusual properties:

It's the only triangle with three angles in 2:2:1 proportions
It's the shape of the triangles found in the points of pentagrams
It's used to form a logarithmic spiral

Let's find out how to use this tool on a simple example. Have a look at this step-by-step solution:

Determine what is your first given value. Assume we want to check the properties of the golden triangle. Type 1.681 inches into leg box.
Enter second known parameter. For example, take a base equal to 1 in.
All the other parameters are calculated in the blink of an eye! We checked for instance that isosceles triangle perimeter is 4.236 in and that the angles in the golden triangle are equal to 72° and 36° - the ratio is equal to 2:2:1, indeed.

You can use this calculator to determine different parameters than in the example, but remember that there are in general two distinct isosceles triangles with given area and other parameter, e.g. leg length. Our calculator will show one possible solution.

Example Video Questions Lesson

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Example Video Questions Lesson

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The triangle above is isosceles because there are lines marking two of its equal sides.

Angle ‘a’ and the angle marked 50° are opposite the two equal sides.

Angle ‘a’ must be 50° as well.

The two equal angles, 50° and 50°, add to make 100°.

To find angle ‘b’, we subtract 100° from 180°. This equals 80°.

An isosceles triangle is a triangle that has two equal sides and two equal angles. The two equal sides are marked with lines and the two equal angles are opposite these sides.

We can recognise an isosceles triangle because it will have two sides marked with lines.

Below is an example of an isosceles triangle.

It has two equal sides marked with a small blue line.

It has two equal angles marked in red.

We can see that in this above isosceles triangle, the two base angles are the same size.

All isosceles triangles have a line of symmetry in between their two equal sides.

The sides that are the same length are each marked with a short line.

The two equal angles are opposite to the two equal sides.

The angle at which these two marked sides meet is the odd one out and therefore is different to the other two angles.

If we are told that one of these marked angles is 70°, then the other marked angle must also be 70°.

How to Find a Missing Angle in an Isosceles Triangle

To find a missing angle in an isosceles triangle use the following steps:

If the missing angle is opposite a marked side, then the missing angle is the same as the angle that is opposite the other marked side.

If the missing angle is not opposite a marked side, then add the two angles opposite the marked sides together and subtract this result from 180.

This is because all three angles in an isosceles triangle must add to 180°

For example, in the isosceles triangle below, we need to find the missing angle at the top of the triangle.

The two base angles are opposite the marked lines and so, they are equal to each other.

Both base angles are 70 degrees.

The missing angle is not opposite the two marked sides and so, we add the two base angles together and then subtract this result from 180 to get our answer.

70° + 70° = 140°

The two base angles add to make 140°.

Angles in an isosceles triangle add to 180°.

We subtract the 140° from 180° to see what the size of the remaining angle is.

180° – 140° = 40°

The missing angle on the top of this isosceles triangle is 40°.

We can also think, “What angle do we need to add to 70° and 70° to make 180°?”

The answer is 40°.

How to Find Missing Angles in an Isosceles Triangle from only One Angle

If only one angle is known in an isosceles triangle, then we can find the other two missing angles using the following steps:

If the known angle is opposite a marked side, then the angle opposite the other marked side is the same. Add these two angles together and subtract the answer from 180° to find the remaining third angle.

If the known angle is not opposite a marked side, then subtract this angle from 180° and divide the result by two to get the size of both missing angles.

Here is an example of finding two missing angles in an isosceles triangle from just one known angle.

We know that one angle is 50°. This angle is opposite one of the marked sides.

This means that it is the same size as the angle that is opposite the other marked side. This is angle ‘a’.

Therefore angle ‘a’ is 50° too.

Now to find angle ‘b’, we use the fact that all three angles add up to 180°.

To find angle ‘b’, we subtract both 50° angles from 180°. We first add the two 50° angles together.

50° + 50° = 100°

and 180° – 100° = 80°

Angle ‘b’ is 80° because all angles in a triangle add up to 180°.

Here is another example of finding the missing angles in isosceles triangles when one angle is known.

This time, we know the angle that is not opposite a marked side. We have 30°.

We can subtract 30° from 180° to see what angle ‘a’ and ‘b’ add up to.