Question

1. if m∠2 = 125°, m∠12 = 37° and m∠18 = 102°, find the measure of each missing angle. note: a || b

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle2$ are supplementary (linear - pair), so $m\angle1 = 180^{\circ}-m\angle2$. Since $m\angle2 = 125^{\circ}$, then $m\angle1=180 - 125=55^{\circ}$.

Step2: Use corresponding - angle and alternate - angle properties

Since $a\parallel b$, $\angle3$ and $\angle2$ are vertical angles, so $m\angle3 = m\angle2=125^{\circ}$.

Step3: Use linear - pair property

$\angle4$ and $\angle3$ are supplementary. So $m\angle4 = 180 - m\angle3=180 - 125 = 55^{\circ}$.

Step4: Use vertical - angle property

$\angle5$ and $\angle1$ are vertical angles, so $m\angle5=m\angle1 = 55^{\circ}$.

Step5: Use vertical - angle property

$\angle6$ and $\angle2$ are vertical angles, so $m\angle6=m\angle2 = 125^{\circ}$.

Step6: Use corresponding - angle property

$\angle7$ and $\angle1$ are corresponding angles, so $m\angle7=m\angle1 = 55^{\circ}$.

Step7: Use vertical - angle property

$\angle8$ and $\angle7$ are vertical angles, so $m\angle8=m\angle7 = 55^{\circ}$.

Step8: Use corresponding - angle property

$\angle9$ and $\angle3$ are corresponding angles, so $m\angle9=m\angle3 = 125^{\circ}$.

Step9: Use vertical - angle property

$\angle10$ and $\angle9$ are vertical angles, so $m\angle10=m\angle9 = 125^{\circ}$.

Step10: Use vertical - angle property

$\angle11$ and $\angle12$ are vertical angles, so $m\angle11=m\angle12 = 37^{\circ}$.

Step11: Use linear - pair property

$\angle13$ and $\angle12$ are supplementary. So $m\angle13=180 - m\angle12=180 - 37 = 143^{\circ}$.

Step12: Use vertical - angle property

$\angle14$ and $\angle13$ are vertical angles, so $m\angle14=m\angle13 = 143^{\circ}$.

Step13: Use vertical - angle property

$\angle15$ and $\angle12$ are vertical angles, so $m\angle15=m\angle12 = 37^{\circ}$.

Step14: Use linear - pair property

$\angle16$ and $\angle15$ are supplementary. So $m\angle16=180 - m\angle15=180 - 37 = 143^{\circ}$.

Step15: Use vertical - angle property

$\angle17$ and $\angle18$ are vertical angles, so $m\angle17=m\angle18 = 102^{\circ}$.

Answer:

a. $m\angle1 = 55^{\circ}$
b. $m\angle3 = 125^{\circ}$
c. $m\angle4 = 55^{\circ}$
d. $m\angle5 = 55^{\circ}$
e. $m\angle6 = 125^{\circ}$
f. $m\angle7 = 55^{\circ}$
g. $m\angle8 = 55^{\circ}$
h. $m\angle9 = 125^{\circ}$
i. $m\angle10 = 125^{\circ}$
j. $m\angle11 = 37^{\circ}$
k. $m\angle13 = 143^{\circ}$
l. $m\angle14 = 143^{\circ}$
m. $m\angle15 = 37^{\circ}$
n. $m\angle16 = 143^{\circ}$
o. $m\angle17 = 102^{\circ}$