Question

1. if m∠3 = 74, find each measure.

Explanation:

Step1: Vertical - angle property

Vertical angles are equal. $\angle3$ and $\angle1$ are vertical angles, so $m\angle1 = m\angle3=74^{\circ}$.

Step2: Supplementary - angle property

$\angle3$ and $\angle2$ are supplementary (a linear - pair), so $m\angle2 = 180^{\circ}-m\angle3$. Then $m\angle2=180 - 74=106^{\circ}$.

Step3: Vertical - angle property for $\angle4$

$\angle2$ and $\angle4$ are vertical angles, so $m\angle4 = m\angle2 = 106^{\circ}$.

Step4: Corresponding - angle property (assuming parallel lines)

If the two lines are parallel, $\angle3$ and $\angle5$ are corresponding angles, so $m\angle5 = m\angle3 = 74^{\circ}$.

Step5: Vertical - angle property for $\angle6$

$\angle5$ and $\angle6$ are vertical angles, so $m\angle6 = m\angle5 = 74^{\circ}$.

Step6: Supplementary - angle property for $\angle7$

$\angle5$ and $\angle7$ are supplementary, so $m\angle7 = 180 - m\angle5=106^{\circ}$.

Step7: Vertical - angle property for $\angle8$

$\angle7$ and $\angle8$ are vertical angles, so $m\angle8 = m\angle7 = 106^{\circ}$.

Answer:

a. $m\angle1 = 74^{\circ}$
b. $m\angle2 = 106^{\circ}$
c. $m\angle4 = 106^{\circ}$
d. $m\angle5 = 74^{\circ}$
e. $m\angle6 = 74^{\circ}$
f. $m\angle7 = 106^{\circ}$
g. $m\angle8 = 106^{\circ}$