Question

for 17, 18, 19 - keep in mind comments at the top: parallel lines - angle pairs, triangle, for18,19 solve for x first. we will go over #18 with 10 minutes left - make sure you have solved for x by then

1. if (mangle2 = 125^{circ}), (mangle12 = 37^{circ}) and (mangle18 = 102^{circ}), find the measure of each missing angle.

note: (aparallel b)

Explanation:

Step1: Use linear - pair property

$\angle1$ and $\angle2$ form a linear - pair. So, $m\angle1 + m\angle2=180^{\circ}$. Given $m\angle2 = 125^{\circ}$, then $m\angle1=180^{\circ}-125^{\circ}=55^{\circ}$.

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

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

Step4: Use vertical - angles property

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

Step5: Use vertical - angles property

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

Step6: Use alternate - interior angles property

Since $a\parallel b$, $\angle7$ and $\angle12$ are alternate - interior angles. So, $m\angle7 = m\angle12 = 37^{\circ}$.

Step7: Use vertical - angles property

$\angle8$ and $\angle7$ are vertical angles. So, $m\angle8 = m\angle7 = 37^{\circ}$.

Step8: Use linear - pair property

$\angle9$ and $\angle8$ form a linear - pair. So, $m\angle9=180^{\circ}-m\angle8 = 180 - 37 = 143^{\circ}$.

Step9: Use linear - pair property with $\angle12$

$\angle10$ and $\angle12$ form a linear - pair. So, $m\angle10=180^{\circ}-m\angle12 = 180 - 37 = 143^{\circ}$.

Step10: Use vertical - angles property

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

Step11: Use linear - pair property with $\angle18$

$\angle13$ and $\angle18$ form a linear - pair. So, $m\angle13=180^{\circ}-m\angle18 = 180 - 102 = 78^{\circ}$.

Step12: Use vertical - angles property

$\angle14$ and $\angle13$ are vertical angles. So, $m\angle14 = m\angle13 = 78^{\circ}$.

Step13: Use linear - pair property with $\angle14$

$\angle15$ and $\angle14$ form a linear - pair. So, $m\angle15=180^{\circ}-m\angle14 = 180 - 78 = 102^{\circ}$.

Step14: Use vertical - angles property

$\angle16$ and $\angle15$ are vertical angles. So, $m\angle16 = m\angle15 = 102^{\circ}$.

Step15: Use vertical - angles 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. $m\angle7 = 37^{\circ}$
g. $m\angle8 = 37^{\circ}$
h. $m\angle9 = 143^{\circ}$
i. $m\angle10 = 143^{\circ}$
j. $m\angle11 = 37^{\circ}$
k. $m\angle13 = 78^{\circ}$
l. $m\angle14 = 78^{\circ}$
m. $m\angle15 = 102^{\circ}$
n. $m\angle16 = 102^{\circ}$
o. $m\angle17 = 102^{\circ}$