directions: select the relationship between the angle and the given measurement for questions 1-6 by clicking on the small triangles. fill in the measurements of the missing angles. diagrams not drawn to scale
1. diagram with 120°, angles b, c, d, e, f, h, etc. and table for ( m angle d ), ( m angle e ), ( m angle h ), ( m angle c )
2. partially visible diagram and table

Question

Accepted Answer

# Explanation:
## Step1: Find $ m\angle b $ (linear pair with $ 120^\circ $)
A linear pair of angles sums to $ 180^\circ $. So, $ m\angle b = 180^\circ - 120^\circ = 60^\circ $. Since $ \angle d $ and $ \angle b $ are vertical angles (equal), $ m\angle d = 60^\circ $.
## Step2: Find $ m\angle c $ (vertical angle with $ 120^\circ $)
Vertical angles are equal, so $ m\angle c = 120^\circ $.
## Step3: Find $ m\angle e $ (corresponding or alternate - depending on lines, but here $ \angle e $ and $ \angle c $ are same - side interior? Wait, no, the two horizontal lines are parallel (assumed, as it's a transversal setup). $ \angle e $ and the $ 120^\circ $ angle: actually, $ \angle e $ and $ \angle b $ are corresponding? Wait, no, let's re - check. The transversal cuts two parallel lines. $ \angle e $ and $ \angle d $: no, $ \angle e $ and $ \angle c $ are same - side interior? Wait, no, the angle adjacent to $ \angle e $ (let's say $ \angle f $) and $ \angle b $ are corresponding. Wait, maybe better: $ \angle e $ and the $ 120^\circ $ angle: since $ \angle e $ and $ \angle c $ are same - side interior? No, $ \angle c = 120^\circ $, and $ \angle e $ and $ \angle c $ are same - side interior, so they should be supplementary? Wait, no, if the lines are parallel, same - side interior angles are supplementary. Wait, but $ \angle e $ and $ \angle d $: $ \angle d = 60^\circ $, and $ \angle e $ and $ \angle d $ are same - side interior? No, maybe $ \angle e $ is equal to $ \angle c $? Wait, no, let's use vertical angles and linear pairs. $ \angle h $: $ \angle h $ and $ 120^\circ $ angle: $ \angle h $ is equal to $ \angle b $? Wait, no, let's start over.

The angle of $ 120^\circ $ and $ \angle b $ form a linear pair, so $ m\angle b=180 - 120 = 60^\circ $. $ \angle d $ is vertical to $ \angle b $, so $ m\angle d = 60^\circ $. $ \angle c $ is vertical to the $ 120^\circ $ angle, so $ m\angle c = 120^\circ $. Now, for $ \angle e $: since the two horizontal lines are parallel (implied by the transversal), $ \angle e $ and $ \angle c $ are same - side interior angles? No, $ \angle e $ and $ \angle d $: wait, $ \angle e $ and $ \angle b $ are corresponding angles (if lines are parallel), so $ m\angle e = 120^\circ $? Wait, no, I think I made a mistake. Let's look at $ \angle h $: $ \angle h $ and the $ 120^\circ $ angle: $ \angle h $ is equal to $ \angle b $? No, $ \angle h $ and $ \angle d $ are corresponding? Wait, maybe the two horizontal lines are parallel, so $ \angle h $ is equal to $ \angle d $'s supplement? No, let's use the fact that in a transversal cutting parallel lines, corresponding angles are equal, alternate interior angles are equal, and linear pairs sum to $ 180^\circ $.

Wait, the $ 120^\circ $ angle and $ \angle c $ are vertical angles, so $ m\angle c = 120^\circ $. $ \angle c $ and $ \angle e $: if the two horizontal lines are parallel, $ \angle c $ and $ \angle e $ are same - side interior angles, so they are supplementary? No, same - side interior angles are supplementary. So $ m\angle e=180 - 120 = 60^\circ $? Wait, no, that contradicts. Wait, maybe the angle labeled $ 120^\circ $ and $ \angle b $ are adjacent, forming a linear pair, so $ m\angle b = 60^\circ $. Then $ \angle d $ is vertical to $ \angle b $, so $ m\angle d = 60^\circ $. $ \angle e $ is vertical to $ \angle c $? No, $ \angle e $ and $ \angle h $: $ \angle h $ is equal to $ \angle d $'s supplement? Wait, I think I need to correct.

Let's list the angles:

- $ m\angle d $: $ \angle d $ and the $ 120^\circ $ angle? No, $ \angle d $ and $ \angle b $ are vertical angles. The angle of $ 120^\circ $ and $ \angle b $ are linear pair, so $ m\angle b=180 - 120 = 60^\circ $, so $ m\angle d = 60^\circ $.

- $ m\angle e $: $ \angle e $ and $ \angle c $ are vertical angles? No, $ \angle c $ is vertical to the $ 120^\circ $ angle, so $ m\angle c = 120^\circ $. $ \angle e $ and $ \angle c $: if the lines are parallel, $ \angle e $ and $ \angle c $ are same - side interior angles, so $ m\angle e = 180 - 120 = 60^\circ $? No, that's not right. Wait, maybe $ \angle e $ is equal to $ \angle c $'s supplement. Wait, I think I messed up the parallel lines. Let's assume the two horizontal lines are parallel, and the transversal is the slant line. Then:

- $ \angle b $ and $ \angle f $ (the angle adjacent to $ \angle e $) are corresponding angles, so $ m\angle f = 60^\circ $. Then $ \angle e $ and $ \angle f $ are linear pair, so $ m\angle e = 180 - 60 = 120^\circ $.

- $ \angle h $: $ \angle h $ and $ \angle b $ are corresponding angles? No, $ \angle h $ and $ \angle d $ are alternate interior angles? Wait, $ \angle h $ and $ \angle c $ are corresponding? No, let's use vertical angles. $ \angle h $ and $ \angle e $ are linear pair? No, $ \angle h $ and $ \angle f $ are vertical angles? Wait, this is getting confusing. Let's start with the known:

1. $ 120^\circ $ and $ \angle b $: linear pair, so $ m\angle b = 60^\circ $.

2. $ \angle d $ is vertical to $ \angle b $, so $ m\angle d = 60^\circ $.

3. $ \angle c $ is vertical to $ 120^\circ $, so $ m\angle c = 120^\circ $.

4. $ \angle e $: since the two horizontal lines are parallel, $ \angle e $ and $ \angle c $ are same - side interior angles? No, $ \angle e $ and $ \angle d $ are same - side interior? Wait, no, $ \angle e $ and $ \angle c $ are alternate interior? No, alternate interior angles are equal. If $ \angle c = 120^\circ $, and $ \angle e $ is alternate interior to $ \angle c $, then $ m\angle e = 120^\circ $.

5. $ \angle h $: $ \angle h $ is vertical to $ \angle d $? No, $ \angle h $ and $ \angle b $ are corresponding angles, so $ m\angle h = 60^\circ $. Wait, no, $ \angle h $ and $ \angle d $ are corresponding? If the lines are parallel, $ \angle h $ (on the lower line) and $ \angle d $ (on the upper line) are corresponding, so $ m\angle h = 60^\circ $.

So summarizing:

- $ m\angle d = 60^\circ $

- $ m\angle e = 120^\circ $ (because it's vertical to $ \angle c $ or same - side? Wait, no, if $ \angle e $ and $ \angle c $ are alternate interior, then $ m\angle e = 120^\circ $)

- $ m\angle h = 60^\circ $ (corresponding to $ \angle d $)

- $ m\angle c = 120^\circ $ (vertical to $ 120^\circ $ angle)

# Answer:
$ m\angle d = 60^\circ $, $ m\angle e = 120^\circ $, $ m\angle h = 60^\circ $, $ m\angle c = 120^\circ $

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QUESTION IMAGE

Question

Explanation:

Step1: Find \( m\angle b \) (linear pair with \( 120^\circ \))

Step2: Find \( m\angle c \) (vertical angle with \( 120^\circ \))

Answer: