Question

m∠abc = 160° find m∠dbc
(diagram: point b with rays ba (angle 6x+20), bd, and bc (angle 4x))

Explanation:

Step1: Set up the angle sum equation

The measure of ∠ABC is the sum of ∠ABD (which is \(6x + 20\)) and ∠DBC (which is \(4x\)). So we have the equation: \( (6x + 20) + 4x = 160 \).

Step2: Combine like terms

Combine the \(x\) terms: \(6x + 4x + 20 = 160\) simplifies to \(10x + 20 = 160\).

Step3: Solve for \(x\)

Subtract 20 from both sides: \(10x = 160 - 20 = 140\). Then divide both sides by 10: \(x = \frac{140}{10} = 14\).

Step4: Find \(m\angle DBC\)

Since \(m\angle DBC = 4x\), substitute \(x = 14\) into the expression: \(4\times14 = 56\).

Answer:

\(56^\circ\)