Question

1. line a is parallel to line b. line c is parallel to line d. name the angle relationship between the two specified angles and determine the missing angle measures.

a) ∠1 and ∠3
b) ∠1 and ∠4
c) ∠2 and ∠3
d) ∠2 and ∠5
e) ∠2 and ∠4
f) ∠4 and ∠6
g) m∠1 =
h) m∠2 =
i) m∠3 =
j) m∠4 =
k) m∠5 =
l) m∠6 =

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle1$ and the $134^{\circ}$ angle are vertical angles. So $m\angle1 = 134^{\circ}$.

Step2: Identify linear - pair relationship

$\angle1$ and $\angle2$ form a linear - pair. Since the sum of angles in a linear - pair is $180^{\circ}$, $m\angle2=180 - 134=46^{\circ}$.

Step3: Identify corresponding - angle relationship

Corresponding angles are equal when lines are parallel. $\angle1$ and $\angle3$ are corresponding angles, so $m\angle3 = 134^{\circ}$.

Step4: Identify vertical - angle relationship for $\angle2$ and $\angle4$

$\angle2$ and $\angle4$ are vertical angles, so $m\angle4 = 46^{\circ}$.

Step5: Identify alternate - interior angles

$\angle2$ and $\angle5$ are alternate - interior angles. Since the lines are parallel, $m\angle5 = 46^{\circ}$.

Step6: Identify corresponding - angle relationship for $\angle4$ and $\angle6$

$\angle4$ and $\angle6$ are corresponding angles, so $m\angle6 = 46^{\circ}$.

Angle - relationship identification

a) $\angle1$ and $\angle3$: Corresponding angles
b) $\angle1$ and $\angle4$: No special direct relationship
c) $\angle2$ and $\angle3$: No special direct relationship
d) $\angle2$ and $\angle5$: Alternate - interior angles
e) $\angle2$ and $\angle4$: Vertical angles
f) $\angle4$ and $\angle6$: Corresponding angles
g) $m\angle1 = 134^{\circ}$
h) $m\angle2 = 46^{\circ}$
i) $m\angle3 = 134^{\circ}$
j) $m\angle4 = 46^{\circ}$
k) $m\angle5 = 46^{\circ}$
l) $m\angle6 = 46^{\circ}$

Answer:

a) Corresponding angles
b) No special direct relationship
c) No special direct relationship
d) Alternate - interior angles
e) Vertical angles
f) Corresponding angles
g) $134^{\circ}$
h) $46^{\circ}$
i) $134^{\circ}$
j) $46^{\circ}$
k) $46^{\circ}$
l) $46^{\circ}$