Q. 29 WE - Geometry

Question

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

$\mathit{m}\mathbf{\angle }\mathbf{3}\mathbf{=}\mathbf{6}\mathit{x}$, $\mathit{m}\mathbf{\angle }\mathit{K}\mathit{A}\mathit{T}\mathbf{=}\mathbf{90}\mathbf{-}\mathit{x}$

Step-by-Step Solution

Answer

The value of $\mathit{x}$ is ${\mathbf{18}}^{\mathbf{\text{o}}}$.

Step 1 - Line bisector and straight angle

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

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

Step 2 - Observe the figure

The given figure is

From the figure, since $SAT$ is a straight line, therefore,

$m\angle 3+m\angle KAT={180}^{°}$

Step 3 - Calculate x .

In order to calculate the value of $x$, substitute $6x$ for $m\angle 3$ and $90-x$ for $m\angle KAT$ into the equation $m\angle 3+m\angle KAT={180}^{°}$ and simplify.

$\begin{array}{c}6x+{90}^{°}-x={180}^{°}\\ 5x+{90}^{°}={180}^{°}\end{array}$ 

Subtract ${90}^{°}$ from both sides.

$\begin{array}{c}5x+{90}^{°}-{90}^{°}={180}^{°}-{90}^{°}\\ 5x={90}^{°}\\ x=\frac{{90}^{°}}{5}\\ x={18}^{°}\end{array}$ 

Therefore, $x={18}^{°}$.