Question

1. write a series of if - then statements that allow you to find the measure of each angle, given that ∠ilh = 38°. use the definitions of supplementary and complementary angles that you have learned so far. if ①, then ② because they are ③ angles. if ④, then ⑤ because they are ⑥ angles. if ⑦, then ⑧ because they are ⑨ angles. if ⑩, then ⑪ because they are ⑫ angles. m∠flg = 90° m∠klj = 52° m∠ilh = 38° complementary m∠jlj = 90°

Explanation:

Step1: Identify right - angled pair

If $\angle FLG$ is formed as shown, then $m\angle FLG = 90^{\circ}$ because they are right angles.

Step2: Find complementary angle

If $\angle ILH=38^{\circ}$, then $m\angle KLJ = 52^{\circ}$ because they are complementary angles ($90 - 38=52$).

Step3: Find supplementary angle

If $\angle ILH = 38^{\circ}$, then the angle supplementary to $\angle ILH$ (let's say $\angle ILK$) has measure $142^{\circ}$ because they are supplementary angles ($180 - 38 = 142$).

Step4: Vertical - angle relationship

If $\angle ILH$ and $\angle FLK$ are vertical angles, then $m\angle FLK=38^{\circ}$ because they are vertical angles (vertical angles are equal).

Step5: Another vertical - angle relationship

If $\angle KLJ$ and $\angle GLH$ are vertical angles, then $m\angle GLH = 52^{\circ}$ because they are vertical angles.

Answer:

If $\angle FLG$ is as shown, then $m\angle FLG = 90^{\circ}$ because they are right angles. If $\angle ILH=38^{\circ}$, then $m\angle KLJ = 52^{\circ}$ because they are complementary angles. If considering the supplement of $\angle ILH$, then the supplementary - angle measure is $142^{\circ}$ because they are supplementary angles. If $\angle ILH$ and $\angle FLK$ are vertical angles, then $m\angle FLK = 38^{\circ}$ because they are vertical angles. If $\angle KLJ$ and $\angle GLH$ are vertical angles, then $m\angle GLH=52^{\circ}$ because they are vertical angles.