Question

4 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

$m\angle1=m\angle3 = 54^{\circ}$

Step2: Complementary - angles

Since $\angle2$ and $\angle3$ are complementary, $m\angle2 = 90^{\circ}-m\angle3=90 - 54=36^{\circ}$

Step3: Vertical - angles are equal

$m\angle4=m\angle2 = 36^{\circ}$

Step4: Linear - pair

$m\angle5 = 180^{\circ}-m\angle3=180 - 54 = 126^{\circ}$

Step5: Vertical - angles are equal

$m\angle6=m\angle5 = 126^{\circ}$

Step6: Vertical - angles are equal

$m\angle7=m\angle5 = 126^{\circ}$

Step7: Vertical - angles are equal

$m\angle8=m\angle6 = 126^{\circ}$

Step8: Corresponding - angles

Assuming parallel lines, if the lines are parallel, $m\angle9=m\angle3 = 54^{\circ}$

Step9: Vertical - angles are equal

$m\angle10=m\angle9 = 54^{\circ}$

Step10: Linear - pair

$m\angle11 = 180^{\circ}-m\angle9=180 - 54 = 126^{\circ}$

Step11: Vertical - angles are equal

$m\angle12=m\angle11 = 126^{\circ}$

Step12: Corresponding - angles

If the lines are parallel, $m\angle13=m\angle3 = 54^{\circ}$

Step13: Vertical - angles are equal

$m\angle14=m\angle13 = 54^{\circ}$

Answer:

a. $m\angle1 = 54^{\circ}$
b. $m\angle2 = 36^{\circ}$
c. $m\angle4 = 36^{\circ}$
d. $m\angle5 = 126^{\circ}$
e. $m\angle6 = 126^{\circ}$
f. $m\angle7 = 126^{\circ}$
g. $m\angle8 = 126^{\circ}$
h. $m\angle9 = 54^{\circ}$
i. $m\angle10 = 54^{\circ}$
j. $m\angle11 = 126^{\circ}$
k. $m\angle12 = 126^{\circ}$
l. $m\angle13 = 54^{\circ}$
m. $m\angle14 = 54^{\circ}$