in the figure, m∠3 = 75° and m∠10 = 115°. find the measure of each angle. work must be shown clearly and neatly, and may be shown by labeling the diagram.
15) ∠2
16) ∠5
17) ∠7
18) ∠15
19) ∠14
20) ∠9

Question

Accepted Answer

# Explanation:
## Step1: Use vertical - angle property
Vertical angles are equal. $\angle3$ and $\angle1$ are vertical angles, so $m\angle1 = 75^{\circ}$. $\angle10$ and $\angle14$ are vertical angles, so $m\angle14=115^{\circ}$.
## Step2: Use linear - pair property
A linear pair of angles is supplementary (sum to $180^{\circ}$). $\angle1$ and $\angle2$ form a linear pair, so $m\angle2 = 180^{\circ}-m\angle1=180 - 75=105^{\circ}$. $\angle14$ and $\angle9$ form a linear pair, so $m\angle9 = 180^{\circ}-m\angle14=180 - 115 = 65^{\circ}$.
## Step3: Use corresponding - angle, alternate - interior, and alternate - exterior angle relationships (assuming parallel lines or angle - sharing relationships as appropriate)
Since $\angle3$ and $\angle7$ are corresponding angles (assuming appropriate parallel - line setup), $m\angle7 = 75^{\circ}$. $\angle5$ and $\angle10$ are alternate - exterior angles (assuming appropriate parallel - line setup), so $m\angle5 = 115^{\circ}$. $\angle15$ and $\angle9$ are corresponding angles (assuming appropriate parallel - line setup), so $m\angle15 = 65^{\circ}$.

15) $m\angle2 = 105^{\circ}$
16) $m\angle5 = 115^{\circ}$
17) $m\angle7 = 75^{\circ}$
18) $m\angle15 = 65^{\circ}$
19) $m\angle14 = 115^{\circ}$
20) $m\angle9 = 65^{\circ}$

# Answer:
15) $105^{\circ}$
16) $115^{\circ}$
17) $75^{\circ}$
18) $65^{\circ}$
19) $115^{\circ}$
20) $65^{\circ}$

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QUESTION IMAGE

Question

Explanation:

Step1: Use vertical - angle property

Step2: Use linear - pair property

Step3: Use corresponding - angle, alternate - interior, and alternate - exterior angle relationships (assuming parallel lines or angle - sharing relationships as appropriate)

Answer: