Question

2pts: solve for the missing angles in the picture below.

Explanation:

Step1: Use vertical - angle property

$\angle1 = 104^{\circ}$ (Vertical angles are equal)

Step2: Use linear - pair property

$\angle2=180^{\circ}- 104^{\circ}=76^{\circ}$ (Linear - pair of angles sum to $180^{\circ}$)

Step3: Use corresponding - angle property

$\angle3=\angle1 = 104^{\circ}$ (Corresponding angles are equal for parallel lines)
$\angle4=\angle2 = 76^{\circ}$
$\angle5=\angle7$ and $\angle6=\angle8$. Since $\angle7=\angle1 = 104^{\circ}$ (Vertical angles), $\angle5 = 104^{\circ}$ and $\angle6=76^{\circ}$

Step4: For the other set of parallel lines

$\angle14 = 82^{\circ}$ (Vertical angles)
$\angle13=180^{\circ}-82^{\circ}=98^{\circ}$ (Linear - pair)
$\angle11=\angle13 = 98^{\circ}$ (Corresponding angles)
$\angle12=\angle14 = 82^{\circ}$
$\angle9=\angle11 = 98^{\circ}$ and $\angle10=\angle12 = 82^{\circ}$ (Vertical angles)
$\angle15=\angle9 = 98^{\circ}$ and $\angle16=\angle10 = 82^{\circ}$ (Vertical angles)

Answer:

$\angle1 = 104^{\circ}$, $\angle2 = 76^{\circ}$, $\angle3 = 104^{\circ}$, $\angle4 = 76^{\circ}$, $\angle5 = 104^{\circ}$, $\angle6 = 76^{\circ}$, $\angle7 = 104^{\circ}$, $\angle8 = 76^{\circ}$, $\angle9 = 98^{\circ}$, $\angle10 = 82^{\circ}$, $\angle11 = 98^{\circ}$, $\angle12 = 82^{\circ}$, $\angle13 = 98^{\circ}$, $\angle14 = 82^{\circ}$, $\angle15 = 98^{\circ}$, $\angle16 = 82^{\circ}$