Question

Fill in the blank with the correct response. Given ∠1=∠2, find x.

Answer 1

Answer:

x = 6

Step-by-step explanation:

Since, ∠1 ≅ ∠2

By angle bisector theorem,

$\frac{AB}{BD}=\frac{AC}{CD}$

By substituting the measures of each side in the given ratio of the sides,

$\frac{3}{x-4}=\frac{x}{4}$

12 = x(x - 4)

12 = x² - 4x

x² - 4x - 12 = 0

x² - 6x + 2x - 12 = 0

x( x - 6) + 2(x - 6) = 0

(x + 2)(x - 6) = 0

x = -2, 6

Since, measure of the sides can't be negative, x can not be negative.

Therefore, x = 6 will be the answer.