Question

In the figure, find the value of \[x\] and hence find all three indicated angles.

Answer 1

Hint:
We will first consider the figure, we can see from the figure that angle \[5x\] makes the \[90^\circ \] angle. Thus, we will find the value of \[x\] by keeping both the angles equal and then we will substitute the value of \[x\] in the indicated angles.

Complete step by step solution:
We will first consider the given figure,

Let us name the point \[{\text{O}}\] where all the lines are getting intersected.
As we can see from the figure that \[\angle FOB = 5x\] and \[\angle FOB = 90^\circ \].
Thus, we can find the value of \[x\] by putting both the angles equal.
Hence, we get,
\[
   \Rightarrow 5x = 90 \\
   \Rightarrow x = \dfrac{{90}}{5} \\
   \Rightarrow x = 18 \\
 \]
Thus, we get the value of \[x\] as 18.
Next, we can find the other indicated angles using the value of \[x\].
As there are three indicated angles in the figure, they are \[2x,3x\] and \[5x\].
Now, we will substitute the value of \[x\] in these indicated angles.
Thus, we get,
\[
   \Rightarrow 2x = 2\left( {18} \right) = 36^\circ \\
   \Rightarrow 3x = 3\left( {18} \right) = 54^\circ \\
   \Rightarrow 5x = 5\left( {18} \right) = 90^\circ \\
 \]

Hence, the value of \[x\] is 18, \[2x\] is 36, \[3x\] is 54 and \[5x\] is 90.

Note:
We have analyzed the figure and have found that the angle \[5x\] is equal to 90 which helps us in finding all the other values. When the value of \[x\] is evaluated, we can find the other angles easily by multiplying the value of \[x\] with the given indicated angle. The perpendicular angle is of \[90^\circ \]. As the lines are not congruent so we can not consider other angles sum as \[90^\circ \].