what is the measure of $ \angle abd $?
$ 27 ^ { \circ } $
$ 54 ^ { \circ } $
$ 114 ^ { \circ } $
$ 124 ^ { \circ } $

Question

Accepted Answer

# Answer:
C. $114^{\circ}$

# 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, $(4n + 6)^{\circ}=(2n)^{\circ}+60^{\circ}$
## Step2: Solve for $n$
$$
\begin{align*}
4n+6&=2n + 60\
4n-2n&=60 - 6\
2n&=54\
n& = 27
\end{align*}
$$
## Step3: Find the measure of $\angle ABD$
$\angle ABD = 180^{\circ}-(4n + 6)^{\circ}$. Substitute $n = 27$ into $(4n + 6)$
$$
\begin{align*}
4n+6&=4\times27+6\
&=108 + 6\
&=114
\end{align*}
$$
$\angle ABD=180^{\circ}-66^{\circ}=114^{\circ}$ (Since $\angle ABD$ and $(4n + 6)$ are supplementary)

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QUESTION IMAGE

Question

Explanation:

Step1: Apply the exterior angle theorem

Step2: Solve for \(n\)

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

Answer: