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Finding the Missing Angle in an Isosceles Triangle
Published on August 10, 2026
Geometry
Calculate the value of x in an isosceles triangle with a vertex angle of 60 degrees by using the triangle angle sum property.
Question
Answer
To find the value of
- Identify the type of triangle: The image shows a triangle with two sides marked with single tick marks. This indicates that these two sides are equal in length, making it an isosceles triangle.
- Use the properties of isosceles triangles: In an isosceles triangle, the angles opposite the equal sides are also equal. Therefore, the two base angles are equal. One of these base angles is labeled as
, so the other base angle is also . - Sum of angles in a triangle: The sum of the interior angles of any triangle is always
. - Set up the equation: We are given that the vertex angle is
and the two base angles are both . - Solve for
: Subtract from both sides: Divide by 2:
Since all three angles are
Theorems
• Base Angles Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
• Triangle Angle Sum Theorem
The sum of the interior angles of any triangle is always