Question

example 6 given m∠2 = 41°, m∠5 = 94°, and m∠10 = 109°, find the measure of each missing angle.
a. m∠1 =
b. m∠3 =
c. m∠4 =
d. m∠6 =
e. m∠7 =
f. m∠8 =
g. m∠9 =
© gina wilson (all things algebra), 2014

Explanation:

Step1: Vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle2$ are vertical angles, so $m\angle1=m\angle2 = 41^{\circ}$.

Step2: Vertical - angle property

$\angle3$ and $\angle5$ are vertical angles, so $m\angle3=m\angle5 = 94^{\circ}$.

Step3: Vertical - angle property

$\angle4$ and $\angle10$ are vertical angles, so $m\angle4=m\angle10 = 109^{\circ}$.

Step4: Corresponding - angle property

$\angle1$ and $\angle6$ are corresponding angles, so $m\angle6=m\angle1 = 41^{\circ}$.

Step5: Corresponding - angle property

$\angle3$ and $\angle7$ are corresponding angles, so $m\angle7=m\angle3 = 94^{\circ}$.

Step6: Corresponding - angle property

$\angle4$ and $\angle8$ are corresponding angles, so $m\angle8=m\angle4 = 109^{\circ}$.

Step7: Vertical - angle property

$\angle8$ and $\angle9$ are vertical angles, so $m\angle9=m\angle8 = 109^{\circ}$.

Answer:

a. $m\angle1 = 41^{\circ}$
b. $m\angle3 = 94^{\circ}$
c. $m\angle4 = 109^{\circ}$
d. $m\angle6 = 41^{\circ}$
e. $m\angle7 = 94^{\circ}$
f. $m\angle8 = 109^{\circ}$
g. $m\angle9 = 109^{\circ}$