Question

solving for exterior angle measures
what is the measure of ∠abd?
27°
54°
114°
124°

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, \(4m + 6=2m+60\).

Step2: Solve the equation for \(m\)

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

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

The measure of \(\angle ABD\) is \(4m + 6\). Substitute \(m = 27\) into the expression: \(4\times27+6=108 + 6=114^{\circ}\).

Answer:

\(114^{\circ}\) (corresponding to the option \(114^{\circ}\))