Question

solving for exterior angle measures
what is the measure of \\( \angle abd \\)?
\\( 114 ^ { \circ } \\)
\\( 27 ^ { \circ } \\)
\\( 54 ^ { \circ } \\)
\\( 124 ^ { \circ } \\)

Explanation:

Step1: Apply the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(4n + 6=2n+60\).

Step2: Solve the equation for \(n\)

Subtract \(2n\) from both sides: \(4n-2n + 6=2n-2n+60\), which simplifies to \(2n+6 = 60\). Then subtract \(6\) from both sides: \(2n+6 - 6=60 - 6\), so \(2n=54\). Divide both sides by \(2\): \(n = 27\).

Step3: Calculate the measure of \(\angle ABD\)

Substitute \(n = 27\) into \(4n + 6\). So, \(4\times27+6=108 + 6=114\).

Answer:

\(114^{\circ}\)