Question

9/25 angles are awesome circuit
find m<abc =

m∠dba = 118°

Explanation:

Step1: Set up an equation

Since \(m\angle DBA=m\angle DBC + m\angle ABC\), we have \(118=(11x + 3)+(5x+3)\).

Step2: Simplify the right - hand side

Combine like terms: \(118 = 11x+5x + 3+3\), so \(118=16x + 6\).

Step3: Solve for \(x\)

Subtract 6 from both sides: \(118 - 6=16x\), which gives \(112 = 16x\). Then divide both sides by 16: \(x=\frac{112}{16}=7\).

Step4: Find \(m\angle ABC\)

Substitute \(x = 7\) into the expression for \(m\angle ABC\) which is \(5x+3\). So \(m\angle ABC=5\times7 + 3=35 + 3=38^{\circ}\).

Answer:

\(38\)