Below is an equilateral triangle.
Calculate X.
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Below is an equilateral triangle.
Calculate X.
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:
Let's divide both sides by 3:
55
Look at the angles shown in the figure below.
What is their relationship?
\( \)
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.
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.
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.
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 .
Substitute X = 55 back into the original expression: each angle = . Check: ✓
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).
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