Question

you: if m∠3 = 74°, find each measure. note: l || m a. m∠1 = 74° e. m∠6 = b. m∠2 = f. m∠7 = c. m∠4 = g. m∠8 = d. m∠5 =

Explanation:

Step1: Vertical - angles are equal

$\angle3$ and $\angle2$ are vertical - angles. So $m\angle2 = m\angle3=74^{\circ}$

Step2: Supplementary - angles

$\angle2$ and $\angle5$ are supplementary. So $m\angle5 = 180^{\circ}-m\angle2=180 - 74=106^{\circ}$

Step3: Corresponding - angles

$\angle3$ and $\angle7$ are corresponding angles. So $m\angle7 = m\angle3 = 74^{\circ}$

Step4: Vertical - angles

$\angle7$ and $\angle4$ are vertical - angles. So $m\angle4 = m\angle7=74^{\circ}$

Step5: Supplementary - angles

$\angle4$ and $\angle8$ are supplementary. So $m\angle8 = 180^{\circ}-m\angle4=180 - 74 = 106^{\circ}$

Step6: Corresponding - angles

$\angle2$ and $\angle6$ are corresponding angles. So $m\angle6 = m\angle2=74^{\circ}$

Answer:

a. $m\angle1 = 74^{\circ}$
b. $m\angle2 = 74^{\circ}$
c. $m\angle4 = 74^{\circ}$
d. $m\angle5 = 106^{\circ}$
e. $m\angle6 = 74^{\circ}$
f. $m\angle7 = 74^{\circ}$
g. $m\angle8 = 106^{\circ}$