Question

BD bisects angle ABC, measure of angle ABC=5x-4, and measure of angle CBD=2x+10. Angle ABC is a(n) _ angle

Answer 1

Since BD bisects ABC, CBD is half of ABC.  Therefore, 2x+10=(5x-4)/2.  We solve for x.

Multiplying by 2, we have:

4x+20=5x-4

Adding 4 and subtracting 4x, we see that:

x=24

Now, we substitute this in for x to find the value of ABC.  We have:

5*(24)-4

120-4

116

Therefore, 116 is the value of angle ABC.  Since 116 is greater than 90, ABC is an obtuse angle.