BA and BC are opposite rays. BD bisects EBC. If measure of EBD=7x-8 and measure of DBC=5x+10, find measure of EBD
Not sure where A fits into this picture.
But if BD bisects angle EBC, then the two halves are equal, right? So,
7x-8 = 5x+10
Find x, and then you can figure the angle.
To find the measure of EBD, we need to set up an equation using the information given.
We know that BD bisects angle EBC, which means that EBD and DBC are equal in measure. Therefore,
7x - 8 = 5x + 10
To solve for x, we can start by isolating the terms with x on one side:
7x - 5x = 10 + 8
2x = 18
Next, we divide both sides of the equation by 2 to solve for x:
x = 9
Now that we have found the value of x, we can substitute it back into the measure of EBD to find its value:
EBD = 7x - 8
EBD = 7(9) - 8
EBD = 63 - 8
EBD = 55
Therefore, the measure of EBD is 55.
To find the measure of EBD, we need to combine the information given in the problem and solve for the value of x.
Since BD bisects EBC, it means that the measure of EBD is equal to the measure of DBC. Therefore, we can set up an equation:
7x - 8 = 5x + 10
Now, let's solve for x:
First, we'll simplify the equation:
7x - 5x = 10 + 8
2x = 18
Next, we divide both sides of the equation by 2 to solve for x:
2x/2 = 18/2
x = 9
Now that we have found the value of x, we substitute it back into one of the given angle measures to find the measure of EBD:
EBD = 7x - 8
EBD = 7(9) - 8
EBD = 63 - 8
EBD = 55
Therefore, the measure of EBD is 55.