Question

Line /is perpendicular to line m. Find the value of x.(19%towom138°Show Your Workwm138°

Answer 1

`x=29`

Step-by-step explanation

Step 1

as the lines L and M are perpendicular, it means the angle formed is a rigth angle, 90 degrees

so

`19+x+w=90\rightarrow equation(1)`

and, we can see angle W and angle 138, are supplementary (Supplementary angles are two angles with a sum of 180)so

`w+138=180`

to solve for w, subtract 138 in both sides

`\begin{gathered} w+138=180 \\ w+138-138=180-138 \\ w=42 \end{gathered}`

Step 2

now, to solve for x, replace the w value in equation (1)

`\begin{gathered} 19+x+w=90\rightarrow equation(1) \\ 19+x+42=90\rightarrow equation(1) \\ \text{add like terms} \\ 61+x=90 \\ \text{subtract 61 in both sides} \\ 61+x-61=90-61 \\ x=29 \end{gathered}`

therefore, the answer is

x=29

I hope this helps you