Q33. - Geometry

Question

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

$\mathit{m}\mathbf{\angle }\mathbf{1}\mathbf{=}\mathbf{2}\mathit{x}\mathbf{-}\mathbf{8}$, $\mathit{m}\mathbf{\angle }\mathbf{3}\mathbf{=}\mathbf{116}$

Step-by-Step Solution

Answer

The value of $\mathit{x}\mathbf{=}\mathbf{20}\mathbf{°}$.

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,  $m\angle 1=m\angle 2=2x-8.$ 

Also $\angle SAT$ is a straight angle therefore,

$m\angle 1+m\angle 2+m\angle 3=180°$

Step 3 - Calculate x .

In order to calculate the value of $x$, substitute $2x-8$ for $m\angle 1$, $2x-8$ for $m\angle 2$, 116 for $m\angle 3$ into the equation $m\angle 1+m\angle 2+m\angle 3=180°$ and simplify.

$$\begin{gathered} 2x-8+2x-8+116=180° \\ 4x-16=180°-116 \\ 4x=80 \\ x=20° \end{gathered}$$

Therefore, $x=20°$