Question

What is the measure of angle \[X\] for the following triangle?

A. \[30\]degrees
B. \[40\] degrees
C. \[50\] degrees
D. \[60\] degrees

Answer 1

Hint: We know that if all the three sides of the triangle are equal, then the triangle is said to be an equilateral triangle. We know that if all three sides of the triangle are equal then all the three angles are equal. We know that the sum of all angles in a triangle is equal to \[{{180}^{\circ }}\]. By using these concepts, this problem can be solved.

Complete step by step solution:
From the question, we were given to find the angle X for the given triangle.
From the diagram, it is clear that all the three sides of the triangle.
We know that if all the three sides of the triangle are equal, then the triangle is said to be an equilateral triangle.
We know that if all three sides of the triangle are equal then all the three angles are equal.
So, by applying this concept to the given triangle we can say that
\[\angle X=\angle Y=\angle Z=C\]
Let us assume this as equation (1).
\[\angle X=\angle Y=\angle Z=C......(1)\]
We know that the sum of all angles in a triangle is equal to \[{{180}^{\circ }}\].
By applying this concept to the given concept, we can say that
\[\angle X+\angle Y+\angle Z={{180}^{\circ }}\]
Let us assume this as equation (2).
\[\angle X+\angle Y+\angle Z={{180}^{\circ }}......(2)\]
Now let us substitute equation (2) in equation (1), then we get
\[\begin{align}
  & \Rightarrow C+C+C={{180}^{\circ }} \\
 & \Rightarrow 3C={{180}^{\circ }} \\
 & \Rightarrow C={{60}^{\circ }} \\
\end{align}\]
Let us assume this as equation (3).
\[\Rightarrow C={{60}^{\circ }}.....(3)\]
Now let us substitute equation (3) in equation (1), then we get
\[\Rightarrow \angle X={{60}^{\circ }}\]
So, it is clear that the measure of angle X for the following triangle \[{{60}^{\circ }}\].

Note: Students may have a calculation mistake while solving this problem. If a small mistake is done, then the final answer may get interrupted. So, these mistakes should be avoided while solving the problem. Students may have a misconception that the sum of all angles in a triangle is equal to \[{{90}^{\circ }}\]. If this misconception is followed, then the final answer will get interrupted.