Question

1. if m∠3 = 54°, find each measure.

a. m∠1=
b. m∠2=
c. m∠4=
d. m∠5=
e. m∠6=
f. m∠7=
g. m∠8=
h. m∠9=
i. m∠10=
j. m∠11=
k. m∠12=
l. m∠13=
m. m∠14=

Explanation:

Step1: Vertical - angles are equal

$\angle3$ and $\angle1$ are vertical - angles, so $m\angle1 = m\angle3=54^{\circ}$

Step2: Linear - pair of angles

$\angle3$ and $\angle2$ form a linear - pair. Since the sum of angles in a linear - pair is $180^{\circ}$, $m\angle2 = 180^{\circ}-m\angle3=180 - 54=126^{\circ}$

Step3: Vertical - angles are equal

$\angle2$ and $\angle4$ are vertical - angles, so $m\angle4 = m\angle2 = 126^{\circ}$

Step4: Vertical - angles are equal

$\angle3$ and $\angle5$ are vertical - angles, so $m\angle5 = m\angle3=54^{\circ}$

Step5: Vertical - angles are equal

$\angle2$ and $\angle6$ are vertical - angles, so $m\angle6 = m\angle2 = 126^{\circ}$

Step6: Vertical - angles are equal

$\angle1$ and $\angle7$ are vertical - angles, so $m\angle7 = m\angle1=54^{\circ}$

Step7: Vertical - angles are equal

$\angle2$ and $\angle8$ are vertical - angles, so $m\angle8 = m\angle2 = 126^{\circ}$

Step8: Vertical - angles are equal

$\angle1$ and $\angle9$ are vertical - angles, so $m\angle9 = m\angle1=54^{\circ}$

Step9: Vertical - angles are equal

$\angle2$ and $\angle10$ are vertical - angles, so $m\angle10 = m\angle2 = 126^{\circ}$

Step10: Vertical - angles are equal

$\angle1$ and $\angle11$ are vertical - angles, so $m\angle11 = m\angle1=54^{\circ}$

Step11: Vertical - angles are equal

$\angle2$ and $\angle12$ are vertical - angles, so $m\angle12 = m\angle2 = 126^{\circ}$

Step12: Vertical - angles are equal

$\angle1$ and $\angle13$ are vertical - angles, so $m\angle13 = m\angle1=54^{\circ}$

Step13: Vertical - angles are equal

$\angle2$ and $\angle14$ are vertical - angles, so $m\angle14 = m\angle2 = 126^{\circ}$

Answer:

a. $m\angle1 = 54^{\circ}$
b. $m\angle2 = 126^{\circ}$
c. $m\angle4 = 126^{\circ}$
d. $m\angle5 = 54^{\circ}$
e. $m\angle6 = 126^{\circ}$
f. $m\angle7 = 54^{\circ}$
g. $m\angle8 = 126^{\circ}$
h. $m\angle9 = 54^{\circ}$
i. $m\angle10 = 126^{\circ}$
j. $m\angle11 = 54^{\circ}$
k. $m\angle12 = 126^{\circ}$
l. $m\angle13 = 54^{\circ}$
m. $m\angle14 = 126^{\circ}$