Question

example 3 given m∠5 = 82°, find the measure of each missing angle.
a. m∠1=
b. m∠2=
c. m∠3=
d. m∠4=
e. m∠6=
f. m∠7=
g. m∠8=
h. m∠9=
i. m∠10=
j. m∠11=
k. m∠12=
example 4 given m∠12 = 121° and m∠6 = 75°, find the measure of each missing angle.

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle1$ and $\angle5$ are vertical angles. Given $m\angle5 = 82^{\circ}$, so $m\angle1=82^{\circ}$.

Step2: Identify corresponding - angle relationship

$\angle1$ and $\angle3$ are corresponding angles. Corresponding angles are equal when lines are parallel. So $m\angle3 = 82^{\circ}$.

Step3: Use linear - pair relationship

$\angle1$ and $\angle2$ form a linear pair. A linear - pair of angles is supplementary, i.e., $m\angle1 + m\angle2=180^{\circ}$. Since $m\angle1 = 82^{\circ}$, then $m\angle2=180 - 82=98^{\circ}$.
$\angle2$ and $\angle4$ are vertical angles, so $m\angle4 = 98^{\circ}$.
$\angle5$ and $\angle6$ are vertical angles, so $m\angle6 = 82^{\circ}$.
$\angle6$ and $\angle8$ are vertical angles, so $m\angle8 = 82^{\circ}$.
$\angle5$ and $\angle7$ are corresponding angles, so $m\angle7 = 82^{\circ}$.
$\angle7$ and $\angle9$ are vertical angles, so $m\angle9 = 82^{\circ}$.
$\angle10$ and $\angle6$ are corresponding angles, so $m\angle10 = 82^{\circ}$.
$\angle11$ and $\angle7$ are corresponding angles, so $m\angle11 = 82^{\circ}$.
$\angle12$ and $\angle8$ are corresponding angles, so $m\angle12 = 82^{\circ}$.

For Example 4:

Step1: Identify vertical - angle relationship

$\angle6$ and $\angle8$ are vertical angles. Given $m\angle6 = 75^{\circ}$, so $m\angle8 = 75^{\circ}$.
$\angle12$ and $\angle10$ are vertical angles. Given $m\angle12 = 121^{\circ}$, so $m\angle10 = 121^{\circ}$.

Step2: Use linear - pair relationship

$\angle6$ and $\angle7$ form a linear pair. So $m\angle7=180 - 75 = 105^{\circ}$.
$\angle7$ and $\angle9$ are vertical angles, so $m\angle9 = 105^{\circ}$.
$\angle12$ and $\angle11$ form a linear pair. So $m\angle11=180 - 121 = 59^{\circ}$.
$\angle11$ and $\angle5$ are vertical angles, so $m\angle5 = 59^{\circ}$.
$\angle5$ and $\angle1$ are corresponding angles, so $m\angle1 = 59^{\circ}$.
$\angle1$ and $\angle3$ are vertical angles, so $m\angle3 = 59^{\circ}$.
$\angle2$ and $\angle3$ form a linear pair, so $m\angle2=180 - 59 = 121^{\circ}$.
$\angle2$ and $\angle4$ are vertical angles, so $m\angle4 = 121^{\circ}$.

Answer:

Example 3:
a. $m\angle1 = 82^{\circ}$
b. $m\angle2 = 98^{\circ}$
c. $m\angle3 = 82^{\circ}$
d. $m\angle4 = 98^{\circ}$
e. $m\angle6 = 82^{\circ}$
f. $m\angle7 = 82^{\circ}$
g. $m\angle8 = 82^{\circ}$
h. $m\angle9 = 82^{\circ}$
i. $m\angle10 = 82^{\circ}$
j. $m\angle11 = 82^{\circ}$
k. $m\angle12 = 82^{\circ}$

Example 4:
a. $m\angle1 = 59^{\circ}$
b. $m\angle2 = 121^{\circ}$
c. $m\angle3 = 59^{\circ}$
d. $m\angle4 = 121^{\circ}$
e. $m\angle5 = 59^{\circ}$
f. $m\angle7 = 105^{\circ}$
g. $m\angle8 = 75^{\circ}$
h. $m\angle9 = 105^{\circ}$
i. $m\angle10 = 121^{\circ}$
j. $m\angle11 = 59^{\circ}$
k. $m\angle12 = 121^{\circ}$