Question

a) state the angle relationship write an equation & solve for the indicated variable and c) find the angle

Answer 1

Notice that the given angles form a straight angle, therefore:

`(5x+4)^(\circ)+(x-2)^(\circ)+(3x+7)^(\circ)=180^(\circ).`

Then:

`5x+4+x-2+3x+7=180.`

Solving the above equation for x we get:

`\begin{gathered} 9x+9=180, \\ 9x=180-9=171, \\ x=19. \end{gathered}`

Answer: The angles are:

`\begin{gathered} (5\cdot19+4)^(\circ)=99^(\circ), \\ (19-2)^(\circ)=17^(\circ), \\ (3\cdot19+7)=64^(\circ). \end{gathered}`