for each part below, use the figure to fill in the blank. if necessary, you may learn what the markings on a…

Explanation:

Step1: Identify triangle type for (a)

In the first - triangle, since two angles are marked as equal, it is an isosceles triangle. In an isosceles triangle, the sides opposite the equal angles are equal. Since $HG = 9$, then $HI=HG$. $HI = 9$

Step2: Identify triangle type for (b)

In the second - triangle, $LK = KJ=13$, so it is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. Let $\angle L=\angle J = 35^{\circ}$. Using the angle - sum property of a triangle ($\angle L+\angle K+\angle J = 180^{\circ}$), we can find $\angle K$. $m\angle K=180^{\circ}-2\times35^{\circ}$ $m\angle K = 180^{\circ}-70^{\circ}=110^{\circ}$

Answer:

(a) $HI = 9$ (b) $m\angle K = 110$