Question

Solve for x. Using that value, find the measurement of

Answer 1

Given: Four corners of a perpendicular intersection

`\begin{gathered} m\angle ABE=(6x+2)^0 \\ m\angle DBE=40^0 \end{gathered}`

To Determine: The value of x and the measure of angle m∠ABE

From the given diagram, it can be seen that m∠ABE and m∠DBE are in one of the four corners of the perpendicular intersection.

Also note that all four corners of a perpendicular intersection is a right angle. Therefore:

`\begin{gathered} m\angle ABE+m\angle DBE=90^0 \\ 6x+2^0+40^0=90^0_{} \\ 6x+42^0=90^0 \\ 6x=90^0-42^0 \\ 6x=48^0 \\ x=(48^0)/(6) \\ x=8^0 \end{gathered}`
`\begin{gathered} m\angle ABE=6x+2 \\ m\angle ABE=6(8)+2 \\ m\angle ABE=48+2 \\ m\angle ABE=50^0 \end{gathered}`

Hence:

x = 8⁰

m∠ABE = 50⁰