Question

jumpstart
name:____
date:____
n ∠1 = ____°
e ∠2 = ____°
r ∠3 = ____°
o ∠4 = ____°
t ∠5 = ____°
i ∠6 = ____°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle4$ and the $100^{\circ}$ angle are vertical angles, so $\angle4 = 100^{\circ}$.

Step2: Use linear - pair property

$\angle2$ and $\angle4$ form a linear - pair (sum is $180^{\circ}$). So $\angle2=180 - 100=80^{\circ}$.

Step3: Use corresponding - angle property

Assume the two horizontal lines are parallel. $\angle5$ and the $35^{\circ}$ angle are corresponding angles, so $\angle5 = 35^{\circ}$.

Step4: Use linear - pair property for $\angle1$ and $\angle5$

$\angle1$ and $\angle5$ form a linear - pair. So $\angle1=180 - 35 = 145^{\circ}$.

Step5: Use vertical - angle property for $\angle3$ and $\angle1$

$\angle3$ and $\angle1$ are vertical angles. So $\angle3=\angle1 = 145^{\circ}$.

Step6: Use vertical - angle property for $\angle6$ and $\angle5$

$\angle6$ and $\angle5$ are vertical angles. So $\angle6=\angle5 = 35^{\circ}$.

Answer:

$\angle1 = 145^{\circ}$
$\angle2 = 80^{\circ}$
$\angle3 = 145^{\circ}$
$\angle4 = 100^{\circ}$
$\angle5 = 35^{\circ}$
$\angle6 = 35^{\circ}$