If m<ABD=2x+5,m<DBC=3x-7, and m<ABC = 73, find x
To find the value of x, we need to use the fact that the sum of the angles in a triangle is 180 degrees.
First, let's find the measures of angles ABD and DBC.
Given m<ABD = 2x + 5,
and m<DBC = 3x - 7.
The sum of angles ABD, DBC, and ABC is equal to 180 degrees.
So, we can write the equation:
(2x + 5) + (3x - 7) + 73 = 180.
Now, let's solve for x:
2x + 5 + 3x - 7 + 73 = 180
5x + 71 = 180
5x = 180 - 71
5x = 109.
To isolate x, divide both sides of the equation by 5:
5x/5 = 109/5
x = 21.8.
Therefore, x is equal to 21.8.