Calculate Angle X in an Equilateral Triangle: Interior Angle Problem

Interior Angles with Equilateral Triangle Properties

Calculate the size of angle X given that the triangle is equilateral.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the value of X
00:03 In an equilateral triangle all angles are equal
00:06 The sum of angles in a triangle equals 180
00:09 Therefore the angle multiplied by 3 should equal 180
00:12 Isolate X
00:15 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Calculate the size of angle X given that the triangle is equilateral.

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2

Step-by-step solution

Remember that the sum of angles in a triangle is equal to 180.

In an equilateral triangle, all sides and all angles are equal to each other.

Therefore, we will calculate as follows:

x+x+x=180 x+x+x=180

3x=180 3x=180

We divide both sides by 3:

x=60 x=60

3

Final Answer

60

Key Points to Remember

Essential concepts to master this topic
  • Rule: All angles in equilateral triangle are equal
  • Technique: Set up equation 3x = 180° then divide by 3
  • Check: Verify 60° + 60° + 60° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Assuming only two angles are equal
    Don't treat this as isosceles with only two equal angles = wrong answer 90°! Equilateral means ALL three sides and ALL three angles are identical. Always remember equilateral triangles have three 60° angles.

Practice Quiz

Test your knowledge with interactive questions

Look at the angles shown in the figure below.

What is their relationship?

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FAQ

Everything you need to know about this question

What's the difference between equilateral and isosceles triangles?

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Equilateral triangles have all three sides equal AND all three angles equal (60° each). Isosceles triangles have only two equal sides and two equal angles.

Why are all angles in an equilateral triangle 60°?

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Since all three angles are equal, we can write x+x+x=180° x + x + x = 180° , which gives us 3x=180° 3x = 180° . Dividing by 3: x=60° x = 60°

Do I always need to set up an equation for this?

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Not really! Once you know it's an equilateral triangle, you can immediately say each angle is 60°. But setting up the equation helps you understand why it's always 60°.

What if the diagram looks different but says equilateral?

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Trust the given information! Even if the triangle doesn't look perfectly equilateral in the drawing, if the problem states it's equilateral, then all angles are 60°.

Can an equilateral triangle have angles other than 60°?

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Never! By definition, equilateral triangles always have three 60° angles. If any angle is different, it's not equilateral anymore.

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