Question

name:
class work

1. ∠6 = 68°

find the measures of
∠1 =
∠2 =
∠3 =
∠4 =
∠5 =
∠7 =
∠8 =

1. complete the statements

∠1 = ∠_ = ∠_ = ∠_
∠2 = ∠_ = ∠_ = ∠_

Explanation:

Step1: Identify vertical - angle relationships

Vertical angles are equal. $\angle 5$ and $\angle 6$ are vertical angles, so $\angle 5=\angle 6 = 68^{\circ}$. Also, $\angle 7$ and $\angle 8$ are vertical angles, and $\angle 1$ and $\angle 4$, $\angle 2$ and $\angle 3$ are vertical angles.

Step2: Identify corresponding - angle relationships

If two parallel lines are cut by a transversal, corresponding angles are equal. $\angle 1$ and $\angle 5$ are corresponding angles, so $\angle 1=\angle 5 = 68^{\circ}$.

Step3: Use linear - pair relationships

A linear pair of angles add up to $180^{\circ}$. Since $\angle 1$ and $\angle 2$ form a linear pair, $\angle 2=180^{\circ}-\angle 1=180 - 68=112^{\circ}$.

Step4: Find other angles

Since $\angle 3$ is vertical to $\angle 2$, $\angle 3=\angle 2 = 112^{\circ}$, and $\angle 4$ is vertical to $\angle 1$, $\angle 4=\angle 1 = 68^{\circ}$. Also, $\angle 7$ is vertical to $\angle 5$, so $\angle 7=\angle 5 = 68^{\circ}$, and $\angle 8$ is vertical to $\angle 6$, so $\angle 8=\angle 6 = 68^{\circ}$.

Step5: Complete the equal - angle statements

$\angle 1=\angle 5=\angle 4=\angle 8$; $\angle 2=\angle 3=\angle 6=\angle 7$

Answer:

1. $\angle 1 = 68^{\circ}$

$\angle 2 = 112^{\circ}$
$\angle 3 = 112^{\circ}$
$\angle 4 = 68^{\circ}$
$\angle 5 = 68^{\circ}$
$\angle 7 = 68^{\circ}$
$\angle 8 = 68^{\circ}$

1. $\angle 1=\angle 5=\angle 4=\angle 8$

$\angle 2=\angle 3=\angle 6=\angle 7$