Question

if bd⊥ac, m∠dbe=(2x - 1)°, and m∠cbe=(5x - 42)°, find the value of x.

Explanation:

Step1: Identify angle - relationship

Since \(BD\perp AC\), \(\angle DBC = 90^{\circ}\). And \(\angle CBE=\angle DBE + \angle DBC\).
So, \((5x - 42)=(2x - 1)+90\).

Step2: Solve the equation

First, expand the right - hand side: \(5x-42 = 2x-1 + 90\).
Then, simplify the right - hand side: \(5x-42=2x + 89\).
Next, subtract \(2x\) from both sides: \(5x-2x-42=2x-2x + 89\), which gives \(3x-42 = 89\).
Then, add 42 to both sides: \(3x-42 + 42=89 + 42\), so \(3x=131\).
Finally, divide both sides by 3: \(x=\frac{131}{3}\).

Answer:

\(x = \frac{131}{3}\)