Answer:
x = 12
Explanation:
An exterior angle of a triangle is equal to the sum of its opposite interior angles in a triangle
∠CBV is an exterior angle and ∠BCD and ∠CDB are ∠CBV's opposite interior angles
This means that ∠BCD + ∠CDB = ∠CBV
If we are given that ∠CBV = 9x - 3, ∠BCD = 5x + 15 and ∠CDB = 30
Then 9x - 3 = 5x + 15 + 30
^ (Note that we just created an equation we can use to solve
for x )
We then use the equation we created to solve for x
9x - 3 = 5x + 15 + 30
step 1 combine like terms
30 + 15 = 45
we now have 9x - 3 = 5x + 45
step 2 add 3 to each side
-3 + 3 cancels out
45 + 3 = 48
we now have 9x = 5x + 48
step 3 subtract 5x from each side
9x - 5x = 4x
5x - 5x cancels out
we now have 4x = 48
step 4 divide each side by 4
48 / 4 = 12
4x / 4 = x
we're left with x = 12