Q. 30 WE - Geometry

Question

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

$\mathit{m}\mathbf{\angle }\mathbf{1}\mathbf{=}\mathbf{7}\mathit{x}\mathbf{+}\mathbf{3}$, $\mathit{m}\mathbf{\angle }\mathbf{2}\mathbf{=}\mathbf{6}\mathit{x}\mathbf{+}\mathbf{7}$

Step-by-Step Solution

Answer

The value of $x$ is $4°$.

Step 1 - Line bisector and straight angle

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

Measure of straight angle is ${180}^{\text{o}}$.

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 $7x+3$ for $m\angle 1$ and $6x+7$ for $m\angle 2$ into the equation $m\angle 1=m\angle 2$ and simplify.

$\begin{array}{c}7x+3=6x+7\\ 7x+3-6x=6x+7-6x\\ x+3=7\\ x+3-3=7-3\\ x=4\end{array}$ 

Therefore, $x=4^{°}$.