Question

1. if m∠2 = 125°, m∠12 = 37° and m∠18 = 102°, find the measure of each missing angle. note: a || b a. m∠1 = f. m∠7 = k. m∠13 = b. m∠3 = g. m∠8 = l. m∠14 = c. m∠4 = h. m∠9 = m. m∠15 = d. m∠5 = i. m∠10 = n. m∠16 = e. m∠6 = j. m∠11 = o. m∠17 =

Explanation:

Step1: Use linear - pair property

$\angle1$ and $\angle2$ form a linear - pair. Since a linear - pair of angles is supplementary ($m\angle1 + m\angle2=180^{\circ}$), and $m\angle2 = 125^{\circ}$, then $m\angle1=180 - 125=55^{\circ}$.

Step2: Use corresponding - angles property

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

Step3: Use linear - pair property for $\angle3$ and $\angle4$

$\angle3$ and $\angle4$ form a linear - pair. So $m\angle4 = 180 - m\angle3=180 - 125 = 55^{\circ}$.

Step4: Use vertical - angles property

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

Step5: Use linear - pair property for $\angle5$ and $\angle6$

$\angle5$ and $\angle6$ form a linear - pair. So $m\angle6=180 - m\angle5=180 - 55 = 125^{\circ}$.

Step6: Use corresponding - angles property

$\angle7$ and $\angle12$ are corresponding angles. So $m\angle7=m\angle12 = 37^{\circ}$.

Step7: Use linear - pair property for $\angle7$ and $\angle8$

$\angle7$ and $\angle8$ form a linear - pair. So $m\angle8=180 - m\angle7=180 - 37 = 143^{\circ}$.

Step8: Use vertical - angles property

$\angle9$ and $\angle7$ are vertical angles. So $m\angle9=m\angle7 = 37^{\circ}$.

Step9: Use linear - pair property for $\angle9$ and $\angle10$

$\angle9$ and $\angle10$ form a linear - pair. So $m\angle10=180 - m\angle9=180 - 37 = 143^{\circ}$.

Step10: Use vertical - angles property

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

Step11: Given $\angle12 = 37^{\circ}$

$m\angle12 = 37^{\circ}$ (given).

Step12: Use linear - pair property for $\angle12$ and $\angle13$

$\angle12$ and $\angle13$ form a linear - pair. So $m\angle13=180 - m\angle12=180 - 37 = 143^{\circ}$.

Step13: Use corresponding - angles property

$\angle14$ and $\angle13$ are corresponding angles. So $m\angle14=m\angle13 = 143^{\circ}$.

Step14: Use vertical - angles property

$\angle15$ and $\angle11$ are vertical angles. So $m\angle15=m\angle11 = 37^{\circ}$.

Step15: Use linear - pair property for $\angle15$ and $\angle16$

$\angle15$ and $\angle16$ form a linear - pair. So $m\angle16=180 - m\angle15=180 - 37 = 143^{\circ}$.

Step16: Use vertical - angles property

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

Step17: Use linear - pair property for $\angle17$ and $\angle18$

$\angle17$ and $\angle18$ form a linear - pair (already used vertical - angles property to get $m\angle17$ from $m\angle18$).

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. $m\angle7 = 37^{\circ}$
g. $m\angle8 = 143^{\circ}$
h. $m\angle9 = 37^{\circ}$
i. $m\angle10 = 143^{\circ}$
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. $m\angle17 = 102^{\circ}$