Question

3)
92°
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65°
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110°
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Explanation:

Step1: Solve first diagram (vertical lines)

Intersection 1 (left):

• Vertical angles are equal: opposite to $92^\circ$ is $92^\circ$.
• Supplementary angles sum to $180^\circ$: $180^\circ - 92^\circ = 88^\circ$ (the other two angles).

Intersection 2 (right):

• Since horizontal lines are parallel, corresponding angles match left intersection: angles are $92^\circ$, $88^\circ$, $92^\circ$, $88^\circ$.

Step2: Solve second diagram (parallel lines)

Intersection 2 (bottom):

• Vertical angles are equal: opposite to $65^\circ$ is $65^\circ$.
• Supplementary angles sum to $180^\circ$: $180^\circ - 65^\circ = 115^\circ$ (the other two angles).

Intersection 1 (top):

• Since horizontal lines are parallel, corresponding angles match bottom intersection: angles are $65^\circ$, $115^\circ$, $65^\circ$, $115^\circ$.

Step3: Solve third diagram (vertical lines)

Intersection 2 (right):

• Vertical angles are equal: opposite to $110^\circ$ is $110^\circ$.
• Supplementary angles sum to $180^\circ$: $180^\circ - 110^\circ = 70^\circ$ (the other two angles).

Intersection 1 (left):

• Since horizontal lines are parallel, corresponding angles match right intersection: angles are $110^\circ$, $70^\circ$, $110^\circ$, $70^\circ$.

Answer:

1. First diagram (left intersection): $88^\circ$, $92^\circ$, $88^\circ$; (right intersection): $92^\circ$, $88^\circ$, $92^\circ$, $88^\circ$
2. Second diagram (bottom intersection): $115^\circ$, $65^\circ$, $115^\circ$; (top intersection): $65^\circ$, $115^\circ$, $65^\circ$, $115^\circ$
3. Third diagram (right intersection): $70^\circ$, $110^\circ$, $70^\circ$; (left intersection): $110^\circ$, $70^\circ$, $110^\circ$, $70^\circ$