Question

the measure of angle 3 is 145°. use the given angle to find all of the other angle measures. identify the angles as acute, right, obtuse or straight. you can use a, r, o and s.

Explanation:

Step1: Vertical - angle property

Angle 3 and angle 1 are vertical angles, so $\angle1=\angle3 = 145^{\circ}$.

Step2: Supplementary - angle property

Angle 2 and angle 3 are supplementary ($\angle2+\angle3 = 180^{\circ}$), so $\angle2=180 - 145=35^{\circ}$. Angle 4 and angle 3 are also supplementary, so $\angle4 = 35^{\circ}$.

Step3: Corresponding - angle property

Since the lines are parallel, angle 3 and angle 7 are corresponding angles, so $\angle7=\angle3 = 145^{\circ}$. Angle 2 and angle 6 are corresponding angles, so $\angle6=\angle2 = 35^{\circ}$.

Step4: Vertical - angle property for parallel - line angles

Angle 7 and angle 5 are vertical angles, so $\angle5=\angle7 = 145^{\circ}$. Angle 6 and angle 8 are vertical angles, so $\angle8=\angle6 = 35^{\circ}$.

Step5: Classify angles

For $121^{\circ}$: O (Obtuse, since $90^{\circ}<121^{\circ}<180^{\circ}$). For $14^{\circ}$: A (Acute, since $0^{\circ}<14^{\circ}<90^{\circ}$). For $90^{\circ}$: R (Right). For $57^{\circ}$: A (Acute). For $180^{\circ}$: S (Straight). For $133^{\circ}$: O (Obtuse). For $68^{\circ}$: A (Acute). For $175^{\circ}$: O (Obtuse). For $43^{\circ}$: A (Acute). For $106^{\circ}$: O (Obtuse).

Answer:

1: $145^{\circ}$
2: $35^{\circ}$
4: $35^{\circ}$
5: $145^{\circ}$
6: $35^{\circ}$
7: $145^{\circ}$
8: $35^{\circ}$
121°: O
14°: A
90°: R
57°: A
180°: S
133°: O
68°: A
175°: O
43°: A
106°: O