Question

HELP PLEASE ITS GEOMETRY 17. If m∠EBD = 4x + 16 and m∠DBC = 6x + 4, find m∠EBD.

Answer 1

Answer:

$m\angle EBD=40^{\circ}$

Step-by-step explanation:

We have been given a diagram. We are asked to find the measure of angle EBD.

Since ray BD is angle bisector of angle EBC, so measure of angle EBD will be equal to measure of angle DBC.

$m\angle DBC=m\angle EBD$

$6x+4=4x+16$

$6x-4x+4=4x-4x+16$

$2x+4=16$

$2x+4-4=16-4$

$2x=12$

$\frac{2x}{2}=\frac{12}{2}$

$x=6$

To find measure of angle EBD, we will substitute $x=6$ in expression $4x+16$ as:

$m\angle EBD=4(6)+16$

$m\angle EBD=24+16$

$m\angle EBD=40$

Therefore, measure of angle EBD is 40 degrees.