Question

there is a line with points d, b, v in order. from b, a segment goes to c, and from d, a segment goes to c. angle at d: 9x - 2, angle at b between bc and bv: 20x + 5, angle at c: 40°

Explanation:

Step1: Identify the exterior angle theorem

In a triangle, an exterior angle is equal to the sum of the two non - adjacent interior angles. Here, \(\angle VBC\) is an exterior angle of \(\triangle DBC\), so \(20x + 5=(9x - 2)+40\).

Step2: Solve the equation for \(x\)

First, simplify the right - hand side of the equation: \((9x - 2)+40=9x+38\).
So our equation becomes \(20x + 5=9x + 38\).
Subtract \(9x\) from both sides: \(20x-9x + 5=9x-9x + 38\), which gives \(11x+5 = 38\).
Subtract 5 from both sides: \(11x+5 - 5=38 - 5\), so \(11x=33\).
Divide both sides by 11: \(x=\frac{33}{11}=3\).

Answer:

\(x = 3\)