Question

find \\( \angle a b d \\) if \\( \angle a b c=121^{circ} \\) in the given figure.

Explanation:

Step1: Find the value of \(x\)

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, \(7x+16 = 121\).
Subtract \(16\) from both sides: \(7x=121 - 16=105\).
Divide both sides by \(7\): \(x = 15\).

Step2: Calculate \(\angle ABD\)

Substitute \(x = 15\) into the expression for \(\angle ABD\) (\(4x+21\)).
\(\angle ABD=4\times15+21\).
First, calculate \(4\times15 = 60\).
Then, \(60+21=81\).

So, \(\angle ABD = 81^{\circ}\).

Answer:

\(81^{\circ}\)