Question

1. for the picture at the right, the m<abc = 80°. find x, m<abd, and m<dbc.

Explanation:

Step1: Set up the equation

Since \(m\angle ABC=m\angle ABD + m\angle DBC\), we have \((x - 6)+(2x + 20)=80\).

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms on the left - hand side: \(x+2x-6 + 20=80\), which simplifies to \(3x+14 = 80\).

Step3: Isolate the variable term

Subtract 14 from both sides of the equation: \(3x+14-14=80 - 14\), so \(3x=66\).

Step4: Solve for \(x\)

Divide both sides by 3: \(x=\frac{66}{3}=22\).

Step5: Find \(m\angle ABD\)

Substitute \(x = 22\) into the expression for \(m\angle ABD\): \(m\angle ABD=x - 6=22-6 = 16^{\circ}\).

Step6: Find \(m\angle DBC\)

Substitute \(x = 22\) into the expression for \(m\angle DBC\): \(m\angle DBC=2x + 20=2\times22+20=44 + 20=64^{\circ}\).

Answer:

\(x = 22\), \(m\angle ABD=16^{\circ}\), \(m\angle DBC=64^{\circ}\)