Question

∠ bad is bisected by . if m∠ bac = 2 x - 5 and m∠ cad = 145, the value of x is: 75 145 70 150

Answer 1

To find the value of x, use the angle bisector theorem. Set up an equation using the theorem and then solve for x. Hence, x ≈ 75

Step-by-step explanation:

To find the value of x, we can use the angle bisector theorem. In a triangle, when a line bisects an angle, it divides the opposite side into segments that are proportional to the lengths of the adjacent sides. In this case, the bisector line AD divides the side BC into segments BD and DC. Using the angle bisector theorem, we can set up the equation:

BD/DC = AB/AC

Since BD and DC are equal, we can substitute the values:

AB/DC = AC/BD

Substituting the given values, we get:

(2x - 5)/145 = 145/(2x - 5)

Cross-multiplying and simplifying the equation, we get:

145(2x - 5) = 145^2

Now, solve for x:

290x - 725 = 21025

290x = 21750

x ≈ 75