if segment bd bisects angle abc. the measure of angle abc=7x. the measure of angle abd=3x+25 find the measure of angle dbc
175
To find the measure of angle DBC (let's call it y), we can use the fact that angle BDC is supplementary to angle ABD, since segment BD bisects angle ABC.
1. First, let's find the measure of angle ABD.
We are given that the measure of angle ABD is 3x + 25.
2. Next, let's find the measure of angle ABC.
We are given that the measure of angle ABC is 7x.
3. Since segment BD bisects angle ABC, we can use the angle bisector theorem:
The measure of angle ABD is equal to the measure of angle DBC.
4. We can write an equation based on step 3:
3x + 25 = y
5. Since angle DBC and angle BDC are supplementary, we have:
y + (3x + 25) = 180
6. Simplify the equation from step 5 by combining like terms:
3x + y + 25 = 180
7. Rearrange the equation from step 6 to isolate y:
y = 180 - (3x + 25)
8. Simplify the equation from step 7:
y = 180 - 3x - 25
9. Continue simplifying:
y = 155 - 3x
Therefore, the measure of angle DBC (y) is 155 - 3x.