Question

 The angles of the triangle are \[\left( {x + 10^\circ } \right)\], \[\left( {2x - 30^\circ } \right)\] and \[x^\circ \]. Find the value of \[x\]?

Answer 1

Hint: We will first consider the given angles. The three angles of the triangle are given in the question and as we know that the sum of all the angles of a triangle is 180 so, we will add all the angles and put it equal to 180 to evaluate the value of \[x\].

Complete step-by-step answer:
First, consider all the three angles of the triangle that is \[\left( {x + 10} \right),\left( {2x - 30} \right),x\].
Now, the objective is to find the value of \[x\].
So, we will apply the angle sum property in this question which states that the sum of all the angles of the triangle is equal to 180.
Thus, we will add all the angles and put it equal to 180.
Thus, we get,
\[ \Rightarrow x + 10 + 2x - 30 + x = 180\]
Here, we will take the terms containing \[x\] on one side and the constants on the other side,
Thus, we get,
\[
   \Rightarrow x + 2x + x = 180 - 10 + 30 \\
   \Rightarrow 4x = 180 + 20 \\
   \Rightarrow 4x = 200 \\
 \]
We will further simplify the above expression and we get,
\[
   \Rightarrow x = \dfrac{{200}}{4} \\
   \Rightarrow x = 50 \\
 \]
Thus, we can conclude that the value of \[x\] is equal to 50.

Note: We have to remember the property of the angle sum property of the triangle. The triangle has three angles so the sum is equal to 180. While simplifying the expression, taking all the variable terms on one side and constant terms on the other side makes the calculation easier.