Answer: x = 10 or x = -6
Step-by-step explanation: If ray BD bisects <ABC, then <ABD ≅ <DBC.
So we can setup the equation x² - 4x = 60.
To solve this polynomial equation, we need to set it equal to 0.
So we subtract 60 from both sides to get x² - 4x - 60 = 0.
On the left, we have a trinomial in a special form that can
be factored as the product of two binomials.
In the first position of each binomial,
we have the factors of the x squared term, x and x.
In the second position, we're looking for the factors
of -60 that add to -4 which are -10 and +6.
So we have (x - 10)(x + 6) = 0.
Whenever two terms are multiplied together to equal 0,
this means that either one or the other must equal 0.
So if (x - 10)(x + 6) = 0, then either x - 10 = 0 or x + 6 = 0.
Solving each equation from here, we find that x = 10 or x = -6.
If you plug both values of x in for the measures of the angles,
you will find out that both of these give us true statements.