Question

1. if ∠5 = 66°, what other angles also measure 66°? a. ∠1 b. ∠2 c. ∠3 d. ∠4 e. ∠6 f. ∠7 g. ∠8

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle5$ and $\angle7$ are vertical angles, so $\angle7 = 66^{\circ}$.

Step2: Identify corresponding - angle relationship

Corresponding angles are equal when two lines are parallel. $\angle5$ and $\angle1$ are corresponding angles, so $\angle1=66^{\circ}$.

Step3: Identify alternate - interior - angle relationship

Alternate - interior angles are equal when two lines are parallel. $\angle5$ and $\angle3$ are alternate - interior angles, so $\angle3 = 66^{\circ}$.

Step4: Identify alternate - exterior - angle relationship

Alternate - exterior angles are equal when two lines are parallel. $\angle5$ and $\angle8$ are alternate - exterior angles, so $\angle8 = 66^{\circ}$.

Step5: Identify linear - pair relationship

Linear - pair angles are supplementary. $\angle5+\angle6 = 180^{\circ}$, so $\angle6=180 - 66=114^{\circ}$. $\angle2$ and $\angle6$ are vertical angles, so $\angle2 = 114^{\circ}$. $\angle4$ and $\angle2$ are corresponding angles, so $\angle4 = 114^{\circ}$.

Answer:

a. $\angle1 = 66^{\circ}$
b. $\angle2 = 114^{\circ}$
c. $\angle3 = 66^{\circ}$
d. $\angle4 = 114^{\circ}$
e. $\angle6 = 114^{\circ}$
f. $\angle7 = 66^{\circ}$
g. $\angle8 = 66^{\circ}$