Question

1. in the figure below, lines $l_1$ and $l_2$ are parallel, angle 13 = $135^\circ$, and angle 10 = $70^\circ$

drag each angle named on the left to its correct measure on the right.
choices

• angle 1
• angle 9
• angle 6
• angle 18

answers
$135^\circ$
$45^\circ$
$110^\circ$
$65^\circ$
$115^\circ$

Explanation:

Step1: Find Angle 1's measure

Angle 13 and Angle 1 are corresponding angles (since $l_1 \parallel l_2$), so $\text{Angle } 1 = \text{Angle } 13 = 135^\circ$.

Step2: Find Angle 9's measure

Angle 10 and Angle 9 are supplementary (linear pair). Given $\text{Angle } 10 = 70^\circ$, so $\text{Angle } 9 = 180^\circ - 70^\circ = 110^\circ$.

Step3: Find Angle 6's measure

Angle 10 and Angle 6 are alternate interior angles (since $l_1 \parallel l_2$), so $\text{Angle } 6 = \text{Angle } 10 = 70^\circ$. Wait, correct: Angle 13 and its adjacent angle (Angle 14) are supplementary: $\text{Angle }14=180^\circ-135^\circ=45^\circ$. Angle 14 and Angle 6 are corresponding angles? No, correct: Angle 13 and Angle 2 are same-side interior, so Angle 2=45°, Angle 6 and Angle 2 are alternate interior? No, re-calculate: Angle 13=135°, so its vertical angle Angle 16=135°, Angle 16 and Angle 4 are corresponding, so Angle4=135°, Angle6 is supplementary to Angle4: $\text{Angle }6=180^\circ-135^\circ=45^\circ$.

Step4: Find Angle 18's measure

Angle 13 and Angle 18 are same-side interior angles? No, Angle 13 and Angle 14 are supplementary (45°), Angle 18 is vertical to Angle 14, so $\text{Angle }18 = 45^\circ$? No, wait: Angle 13=135°, Angle 18 is corresponding to Angle 7, which is supplementary to Angle1. Angle1=135°, so Angle7=45°, so Angle18=45°? No, correct: Angle 13 and Angle 19 are vertical? No, Angle13 and Angle20 are vertical, Angle19 is supplementary to Angle13: $\text{Angle }19=45^\circ$, Angle18 is vertical to Angle15, which is corresponding to Angle7=45°, so $\text{Angle }18=135^\circ$? No, re-do:
Correct Step1: Angle13=135°, Angle1 and Angle13 are corresponding, so $\text{Angle }1=135^\circ$.
Correct Step2: Angle10=70°, Angle9 + Angle10=180°, so $\text{Angle }9=180-70=110^\circ$.
Correct Step3: Angle13=135°, so Angle14=180-135=45°, Angle14 and Angle6 are corresponding, so $\text{Angle }6=45^\circ$.
Correct Step4: Angle18 and Angle1 are corresponding? No, Angle18 and Angle7 are corresponding, Angle7=180-Angle1=45°? No, Angle1 and Angle2 are supplementary, Angle2=45°, Angle7=Angle2 (vertical), so Angle7=45°, Angle18=Angle7 (corresponding), so $\text{Angle }18=45^\circ$? No, Angle18 is adjacent to Angle17, which is corresponding to Angle1=135°, so Angle17=135°, so Angle18=180-135=45°.

Answer:

• Angle 1: $135^\circ$
• Angle 9: $110^\circ$
• Angle 6: $45^\circ$
• Angle 18: $45^\circ$