Lines BA and BC are opposite rays, Lines BD bisects angle EBC and Line BF bisects angle ABE.
If the measure of angle EBD=4x+16 and the measure of angle DBC=6x+4 find the measure of ange EBD
If the measure of angle ABF =7x-8 and the measure of angle EBF=5x+10 find the measure of angle EBF
I need help
FBA angle
x=6 which means that angle EBC=80
To find the measure of angle EBD, we need to use the fact that lines BA and BC are opposite rays, and line BD bisects angle EBC.
First, let's label the angles:
- angle EBD = 4x + 16
- angle DBC = 6x + 4
Since line BD bisects angle EBC, this means that angle EBD is congruent to angle DBC.
Therefore, we can set up the following equation:
4x + 16 = 6x + 4
To solve for x, we can simplify the equation:
4x - 6x = 4 - 16
-2x = -12
Dividing both sides of the equation by -2, we get:
x = 6
Now that we have the value of x, we can substitute it back into the expression for angle EBD:
angle EBD = 4x + 16 = 4(6) + 16 = 24 + 16 = 40
So, the measure of angle EBD is 40.
Now let's move on to finding the measure of angle EBF using a similar approach.
Given:
- angle ABF = 7x - 8
- angle EBF = 5x + 10
Since line BF bisects angle ABE, this means that angle ABF is congruent to angle EBF.
Therefore, we can set up the following equation:
7x - 8 = 5x + 10
To solve for x, we can simplify the equation:
7x - 5x = 10 + 8
2x = 18
Dividing both sides of the equation by 2, we get:
x = 9
Now that we have the value of x, we can substitute it back into the expression for angle EBF:
angle EBF = 5x + 10 = 5(9) + 10 = 45 + 10 = 55
So, the measure of angle EBF is 55.