Question

ZA and B are vertical angles. If m_A = (3x + 13) and mZB = (5x + 9), then find the measure of ZA.

Answer 1

Step-by-step explanation:

The first thing to do is graph the given points of the equation to find the position of the angles.

A=(3X+13)

B=(5X+9)

Both equations to find the angle z should give me a total of 180 degrees

By adding and joining both equations, we have the following:

`\begin{gathered} (3x+13)+(5x+9)=180 \\ 3x+13+5x+9=180 \\ 3x+5x=180-13-9 \\ 8x=180-22 \\ 8x=158 \\ x=(158)/(8) \\ x=19.75 \end{gathered}`

Now plugging the value of x into the first equation to find the angle A gives us:

`\begin{gathered} A=3(19.75)+13 \\ A=59.25+13 \\ \textcolor{#FF7968}{A=72.25}\text{\textcolor{#FF7968}{ DEGREES}} \\ The\text{ measure }of\text{ the angle A is: 72.25} \\ \end{gathered}`

To check if the measure of angle A is correct, we must also replace x in the second equation to find the value of angle B, which has to give us exactly what is missing to complete the 180 degrees.

`\begin{gathered} B=5(19.75)+9 \\ B=98.75+9 \\ B=107.75 \\ \text{Now adding the angles A y B should give us 180 }degrees. \\ \textcolor{#FF7968}{A=72.25} \\ B=107.75 \\ AB=\textcolor{#FF7968}{72.25}+107.75=\textcolor{#FF7968}{180}\text{\textcolor{#FF7968}{ degrees.}} \end{gathered}`