Question

question 30 (5 points)
find \\( \angle a b d \\) if \\( \angle a b c=121^{\circ} \\) in the given figure.
\\( 71^{\circ} \\)
\\( 36^{\circ} \\)
\\( 18^{\circ} \\)
\\( 81^{\circ} \\)

Explanation:

Step1: Set up the equation

Since \(\angle ABC=\angle ABD+\angle DBC\), we have \((4x + 21)+(3x-5)=121\).
Simplify the left - hand side: \(4x+21 + 3x-5=7x + 16\). So, \(7x+16 = 121\).

Step2: Solve for \(x\)

Subtract \(16\) from both sides: \(7x=121 - 16=105\).
Divide both sides by \(7\): \(x=\frac{105}{7}=15\).

Step3: Calculate \(\angle ABD\)

Substitute \(x = 15\) into the expression for \(\angle ABD\) (\(4x+21\)).
\(\angle ABD=4\times15 + 21=60+21=81^{\circ}\).

Answer:

\(81^{\circ}\)