Q. 31 WE - Geometry

Question

$\overleftrightarrow{\mathit{A}\mathit{L}}$ bisects $\mathit{\angle }\mathit{K}\mathit{A}\mathit{T}$. Find the value of $\mathit{x}$.

$\mathit{m}\mathbf{\angle }\mathbf{1}\mathbf{=}\mathbf{5}\mathit{x}\mathbf{-}\mathbf{12}$,  $\mathit{m}\mathbf{\angle }\mathbf{2}\mathbf{=}\mathbf{3}\mathit{x}\mathbf{+}\mathbf{6}$

Step-by-Step Solution

Answer

The value of $x$ is ${\mathbf{9}}^{\mathbf{\text{o}}}$.

Step 1 - Line bisector and straight angle

If a line bisects angles, it divides it into two equal parts.

Measure of straight angle is $180°$.

Step 2 - Observe the figure

The given figure is

From the figure, since $\overleftrightarrow{AL}$ bisects $\angle KAT$, therefore, $m\angle 1=m\angle 2$.

Step 3 - Calculate x .

In order to calculate the value of $x$, substitute $5x-12$ for $m\angle 1$ and $3x+6$ for $m\angle 2$ into the equation $m\angle 1=m\angle 2$ and simplify.

$\begin{array}{c}5x-12=3x+6\\ 5x-12-3x=3x+6-3x\\ 2x-12=6\\ 2x-12+12=6+12\\ 2x=18\\ \frac{2x}{2}=\frac{18}{2}\\ x=9\end{array}$

Therefore, $x=9^{°}$.