Equilateral Triangle: Solve for X When One Angle is X+5

Equilateral Triangle Angles with Algebraic Expressions

Below is an equilateral triangle.

Calculate X.

X+5X+5X+5AAABBBCCC

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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 the angles in a triangle equals 180
00:09 Therefore 3 times the angle equals 180
00:12 Open the brackets and continue to solve
00:16 Isolate X
00:30 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Below is an equilateral triangle.

Calculate X.

X+5X+5X+5AAABBBCCC

2

Step-by-step solution

Since in an equilateral triangle all sides are equal and all angles are equal. It is also known that in a triangle the sum of angles is 180°, we can calculate X in the following way:

X+5+X+5+X+5=180 X+5+X+5+X+5=180

3X+15=180 3X+15=180

3X=18015 3X=180-15

3X=165 3X=165

Let's divide both sides by 3:

3X3=1653 \frac{3X}{3}=\frac{165}{3}

X=55 X=55

3

Final Answer

55

Key Points to Remember

Essential concepts to master this topic
  • Property: All three angles in an equilateral triangle equal 60°
  • Technique: Set up equation: (X+5) + (X+5) + (X+5) = 180°
  • Check: Substitute X = 55 back: 60° + 60° + 60° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Assuming only one angle equals X+5
    Don't set up just one angle as X+5 and the others as 60° = wrong triangle type! This creates an isosceles triangle, not equilateral. Always remember that in an equilateral triangle, all three angles must be equal, so all three angles equal X+5.

Practice Quiz

Test your knowledge with interactive questions

In a right triangle, the side opposite the right angle is called....?

FAQ

Everything you need to know about this question

Why are all three angles X+5 instead of just one?

+

In an equilateral triangle, all sides are equal AND all angles are equal. If one angle is X+5, then all three angles must be X+5 to maintain the equilateral property.

How do I know the sum of angles is 180°?

+

This is the Triangle Angle Sum Theorem - the interior angles of ANY triangle always add up to exactly 180°. This works for all triangles: equilateral, isosceles, and scalene.

What if I get a different answer when solving?

+

Double-check your algebra! The most common errors are: forgetting to distribute properly, making arithmetic mistakes, or not setting up the equation correctly with all three angles equal.

Why can't the angle just be 60° directly?

+

The problem gives us an algebraic expression X+5 for the angle measure. We need to solve for X first, then we can find that each angle equals 55+5=60° 55 + 5 = 60° .

How do I verify my answer is correct?

+

Substitute X = 55 back into the original expression: each angle = 55+5=60° 55 + 5 = 60° . Check: 60°+60°+60°=180° 60° + 60° + 60° = 180°

What makes this triangle equilateral?

+

An equilateral triangle has three equal sides and three equal angles. Since all angles equal 60°, this confirms it's equilateral (not just isosceles or scalene).

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Angles questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations