Question

5) ZLKM is a right angle. Point X is in the interior of the angle and a ray is drawn fromK through X. If MZMKX = (4x - 2) and m ZXKL = (2x +20)°, then find the measuresof the angles created.

Answer 1

We are given that the angle LKM is a right angle. We will go ahead and display this info graphically as follows:

We are told that a ray originating from point ( X ) forms an interior angle at ( K ). We will add this extra bit to the graphical representation above.

Now the angle < LKM is divided into two parts or we could say divided into two constituent angles known as:

`m\angle\text{ MKX \& m}\angle\text{ XKL}`

We are given angle measure expressions for each of the two constituent angles as follows:

`\begin{gathered} m\angle MKX\text{ = 4x - 2} \\ m\angle XKL\text{ = 2x + 20} \end{gathered}`

From the graphical analysis we can extract that the right angle < LKM is an angle sum of its two constituent angles m
`\textcolor{#FF7968}{\angle LKM}\text{\textcolor{#FF7968}{ = m}}\textcolor{#FF7968}{\angle MKX}\text{\textcolor{#FF7968}{ + m}}\textcolor{#FF7968}{\angle XKL}`We are given the respective angle measures in the problem. We will use the above expression and plug in the respective angle measures as follows:

`\begin{gathered} 90\text{ = ( 4x - 2 ) + ( 2x + 20 )} \\ 90\text{ = 6x + 18} \\ 6x\text{ = 72} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 12 degrees}} \end{gathered}`

We have evaluated the angle measurement variable ( x ). Now we can use this value and determine the constituent angles that were created as follows:

`\begin{gathered} m\angle MKX\text{ = 4}\cdot\text{(}12)\text{ - 2 = 46 degrees} \\ m\angle XKL\text{ = 2}\cdot(12)\text{ + 20 = 44 degrees} \end{gathered}`

The measures of the created angle by the ray ( X ) are:

`\begin{gathered} \textcolor{#FF7968}{m\angle MKX}\text{\textcolor{#FF7968}{ = 46 degrees}} \\ \textcolor{#FF7968}{m\angle XKL}\text{\textcolor{#FF7968}{ = 44 degrees}} \end{gathered}`