Given BK→ bisects ∠ABC, m∠ABK=(8x−13)°, and m∠ABC=(10x+28)° Find ∠KBC
To find the measure of ∠KBC, we need to use the given information and apply the concept of angle bisectors.
First, let's write down the information given:
BK bisects ∠ABC
The angle bisector theorem states that when a line bisects an angle, it divides the angle into two congruent angles. In other words, if BK bisects ∠ABC, then m∠ABK = m∠KBC.
We are also given the measures of ∠ABK and ∠ABC:
m∠ABK = (8x - 13)°
m∠ABC = (10x + 28)°
Using the angle bisector theorem, we can equate the measures of ∠ABK and ∠KBC:
m∠ABK = m∠KBC
Therefore, we can set up an equation:
(8x - 13)° = (10x + 28)°
Now, let's solve this equation to find the value of x.
8x - 13 = 10x + 28
Subtracting 8x from both sides:
-13 = 2x + 28
Subtracting 28 from both sides:
-41 = 2x
Dividing both sides by 2:
-20.5 = x
Now that we have found the value of x, we can substitute it back into the expression for ∠KBC to find its measure:
m∠KBC = (8x - 13)°
m∠KBC = (8(-20.5) - 13)°
m∠KBC = (-164 - 13)°
m∠KBC = -177°
So, the measure of ∠KBC is -177°.
Since BK bisects the angle,
2(8x-13) = 10x+28
x = 9
So now you can calculate m∠KBC = m∠ABK