Question

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

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

Short answer

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

Step-by-step solution

- Line bisector and straight angle

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

Measure of straight angle is $180°$.

- 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,

$m\angle 1+m\angle 2+m\angle 3=180°$

- 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.

role="math" localid="1649246369856" $$\begin{gathered} 2x-8+2x-8+116=180° \\ 4x-16=180°-116 \\ 4x=80 \\ x=20° \end{gathered}$$

Therefore,$x=20°$