Finding Missing Angle x in an Equilateral Triangle

Published on August 10, 2026

Geometry

Calculate the value of angle x in a triangle with two equal sides and a vertex angle of 60 degrees, which reveals an equilateral triangle where x is 60 degrees.

Question

Answer

To solve this problem, we need to analyze the properties of the triangle shown in the image.

1. Analyze the given information:

The triangle has two sides marked with single tick marks. This indicates that those two sides are equal in length. A triangle with at least two equal sides is called an isosceles triangle.
The angle between these two equal sides is given as .
We need to find the value of the angle .

2. Use the properties of an isosceles triangle:

In an isosceles triangle, the angles opposite the equal sides are also equal. Let’s call the two base angles (the ones at the bottom)

and

.
Since the two sides forming the

angle are equal, the angles opposite them must be equal:

3. Use the sum of angles in a triangle:

The sum of the interior angles of any triangle is always

. Therefore:

Since we know

, we can substitute

with

4. Solve for :

Subtract

from both sides:

Divide by

5. Determine the type of triangle:

Since all three angles are

(

), all three sides must also be equal. A triangle where all sides and all angles are equal is called an equilateral triangle.

Final Answer:

Type of triangle: Equilateral triangle

Theorems

• Triangle Angle Sum Theorem

The sum of all interior angles in any triangle is always equal to

• Isosceles Triangle Theorem

If two sides of a triangle are equal, then the angles opposite those sides are also equal (

🚀 Try Free Math Help Now!🏠 Learn More Powerful Features