Question

1. m∠abc=(2x + 50)° solve for x

Explanation:

Step1: Set up angle - sum equation

We know that \(m\angle ABC=(2x + 50)^{\circ}\), and \(m\angle ABC=m\angle ABD+m\angle DBC\). So, \(2x + 50=(x + 30)+70\).

Step2: Simplify the right - hand side

\((x + 30)+70=x+(30 + 70)=x + 100\). The equation becomes \(2x+50=x + 100\).

Step3: Isolate the variable x

Subtract \(x\) from both sides: \(2x - x+50=x - x + 100\), which simplifies to \(x+50 = 100\).

Step4: Solve for x

Subtract 50 from both sides: \(x+50-50=100 - 50\).

Answer:

\(x = 50\)