Ray BD bisects angle ABC so that angle ABD = 2y and angle DBC = 5y - 9. What is the measure of angle ABC?
"bisect" means cut in half, so the two angles are equal
5y - 9 = 2y
solve for y, then find 2y
To find the measure of angle ABC, we need to determine the value of y. We are given that angle ABD is equal to 2y, and angle DBC is equal to 5y - 9.
Since ray BD bisects angle ABC, the measure of angle ABD and angle DBC should be equal.
Therefore, we can set up the following equation:
2y = 5y - 9
To solve for y, we can first simplify the equation:
9 = 5y - 2y
9 = 3y
Next, isolate y by dividing both sides of the equation by 3:
y = 9/3
y = 3
Now that we know the value of y, we can substitute it back into the equation to find the measure of angle ABC:
angle ABC = 2y = 2 * 3 = 6
Therefore, the measure of angle ABC is 6.