Question

1. if m∠9 = 97° and m∠12 = 114°, find each measure. a. m∠1 = b. m∠2 = c. m∠3 = d. m∠4 = e. m∠5 = f. m∠6 = g. m∠7 = h. m∠8 = i. m∠10 = j. m∠11 = k. m∠13 = l. m∠14 = m. m∠15 = n. m∠16 =

Explanation:

Step1: Identify vertical - angle relationships

Vertical angles are equal. $\angle9$ and $\angle5$ are vertical angles, so $m\angle5 = m\angle9=97^{\circ}$.

Step2: Identify linear - pair relationships

$\angle9$ and $\angle10$ form a linear - pair (sum to $180^{\circ}$). So $m\angle10 = 180 - 97=83^{\circ}$. $\angle10$ and $\angle14$ are vertical angles, so $m\angle14 = m\angle10 = 83^{\circ}$.
$\angle12$ and $\angle8$ are vertical angles, so $m\angle8=m\angle12 = 114^{\circ}$.
$\angle12$ and $\angle7$ form a linear - pair, so $m\angle7=180 - 114 = 66^{\circ}$.
$\angle7$ and $\angle3$ are vertical angles, so $m\angle3=m\angle7 = 66^{\circ}$.
$\angle8$ and $\angle4$ are vertical angles, so $m\angle4=m\angle8 = 114^{\circ}$.
$\angle3$ and $\angle2$ form a linear - pair, so $m\angle2=180 - 66 = 114^{\circ}$.
$\angle2$ and $\angle6$ are vertical angles, so $m\angle6=m\angle2 = 114^{\circ}$.
$\angle1$ and $\angle9$ are corresponding angles (assuming parallel lines, if not given, we use angle - relationships), and if we assume the lines are parallel, $m\angle1=m\angle9 = 97^{\circ}$.
$\angle11$ and $\angle7$ are corresponding angles, so $m\angle11=m\angle7 = 66^{\circ}$.
$\angle13$ and $\angle5$ are corresponding angles, so $m\angle13=m\angle5 = 97^{\circ}$.
$\angle15$ and $\angle11$ are vertical angles, so $m\angle15=m\angle11 = 66^{\circ}$.
$\angle16$ and $\angle12$ are vertical angles, so $m\angle16=m\angle12 = 114^{\circ}$.

Answer:

a. $m\angle1 = 97^{\circ}$
b. $m\angle2 = 114^{\circ}$
c. $m\angle3 = 66^{\circ}$
d. $m\angle4 = 114^{\circ}$
e. $m\angle5 = 97^{\circ}$
f. $m\angle6 = 114^{\circ}$
g. $m\angle7 = 66^{\circ}$
h. $m\angle8 = 114^{\circ}$
i. $m\angle10 = 83^{\circ}$
j. $m\angle11 = 66^{\circ}$
k. $m\angle13 = 97^{\circ}$
l. $m\angle14 = 83^{\circ}$
m. $m\angle15 = 66^{\circ}$
n. $m\angle16 = 114^{\circ}$