Question

Need help on number 6 in class pls due td!!!

Answer 1

SOLUTION

Since the line are perpendicular, then

$\angle ABD=90^0$

And

$\begin{gathered} \angle\text{ABD}=\angle EBD+\angle ABE \\ \text{Where } \\ \angle EBD=40^0 \\ \text{and } \\ \angle ABE=(6x+2)^0 \end{gathered}$

Substituting the values, we have

$\begin{gathered} 90^0=40^0+(6x+2)^0 \\ 90-40=6x+2 \\ 50=6x+2 \end{gathered}$

We Now collect like terms

$\begin{gathered} 50-2=6x \\ 48=6x \\ \text{Divide both sides by 6} \\ x=\frac{48}{6} \\ x=8 \end{gathered}$

Hence, The value is x is 8

Then the measure of angle ABE is obtained by substituting the value of x

$\begin{gathered} m\angle ABE=(6x+2)^0 \\ \text{where x=8} \\ m\angle ABE=6(8)+2=48+2=50^0 \end{gathered}$

Therefore, the measure of angle ABE is 50°