Question

Angle ABC is bisected by ray BD. If angle ABD = 4x + 20, and angle ABC = 160 degrees, find the value of X.

a) x = 20
b) x = 30
c) x = 10
d) x = 15

Answer 1

To find the value of x, we can use the property of angle bisectors. Since angle ABC is bisected by ray BD, the measure of angle ABD is equal to the measure of angle CBD. From the given information, we set up an equation and solve for x.

Step-by-step explanation:

To find the value of x, we can use the property of angle bisectors. Since angle ABC is bisected by ray BD, the measure of angle ABD is equal to the measure of angle CBD. According to the problem, angle ABC is 160 degrees and angle ABD is 4x + 20. From this information, we can set up an equation:

4x + 20 = 160

Subtracting 20 from both sides:

4x = 140

Dividing both sides by 4:

x = 35

Therefore, the value of x is 35.