Question

8a. what is the shortest side △abc? justify/explain the answer.
8b. using the drawing above: what is the longest side of △adc?

Explanation:

Step1: Find $\angle ABD$ exterior angle

$\angle ABD = 180^\circ - (47^\circ +25^\circ) = 108^\circ$

Step2: Get $\angle ABC$

$\angle ABC = 180^\circ -108^\circ =72^\circ$

Step3: Calculate $\angle BAC$

$\angle BAC = 180^\circ -(72^\circ +58^\circ) =50^\circ$

Step4: Match side to smallest angle

In $\triangle ABC$, smallest angle is $\angle BAC=50^\circ$, opposite side is $BC$.

Step5: Find $\angle DAC$ for $\triangle ADC$

$\angle DAC =25^\circ +50^\circ =75^\circ$

Step6: Match longest side to largest angle

In $\triangle ADC$, largest angle is $\angle DAC=75^\circ$, opposite side is $DC$.

Answer:

8a. The shortest side of $\triangle ABC$ is $\overline{BC}$.
8b. The longest side of $\triangle ADC$ is $\overline{DC}$.