Question

In the figure below, two lines intersect, m<4=6x+30 and m<1=8x-60. Find the number of degrees in m<3

Answer 1

Step-by-step explanation:

In the diagram, the angles labeled 4 and 1 are on a straight line, thus, they add up to 180 degrees.

`\begin{gathered} m\angle4+m\angle1=180\degree \\ \implies(6x+30)+(8x-60)=180 \end{gathered}`

First, solve for x:

`\begin{gathered} 6x+8x-60+30=180 \\ 14x-30=180 \\ 14x=180+30 \\ 14x=210 \\ x=(210)/(14) \\ x=15 \end{gathered}`

Next, angles 3 and 4 are vertical angles, thus, they are equal.

`\begin{gathered} m\angle3=m\angle4=6x+30 \\ At\text{ x=1}5 \\ m\angle3=6(15)+30=90+30 \\ \implies m\angle3=120\degree \end{gathered}`