Question

example 2 if m∠1 = 65°, find each measure. give your reasoning. a. m∠2 = b. m∠3 = c. m∠4 = d. m∠5 = e. m∠6 = f. m∠7 = g. m∠8 =

Explanation:

Step1: Vertical - angles are equal

$\angle1$ and $\angle3$ are vertical - angles. So $m\angle3=m\angle1 = 65^{\circ}$

Step2: Linear - pair angles are supplementary

$\angle1$ and $\angle2$ form a linear - pair. So $m\angle2 = 180^{\circ}-m\angle1=180 - 65=115^{\circ}$

Step3: Vertical - angles are equal

$\angle2$ and $\angle4$ are vertical - angles. So $m\angle4=m\angle2 = 115^{\circ}$

Step4: Corresponding - angles are equal

$\angle1$ and $\angle5$ are corresponding - angles. So $m\angle5=m\angle1 = 65^{\circ}$

Step5: Vertical - angles are equal

$\angle5$ and $\angle7$ are vertical - angles. So $m\angle7=m\angle5 = 65^{\circ}$

Step6: Linear - pair angles are supplementary

$\angle5$ and $\angle6$ form a linear - pair. So $m\angle6=180^{\circ}-m\angle5 = 180 - 65=115^{\circ}$

Step7: Vertical - angles are equal

$\angle6$ and $\angle8$ are vertical - angles. So $m\angle8=m\angle6 = 115^{\circ}$

Answer:

a. $m\angle2 = 115^{\circ}$, Reason: Linear - pair with $\angle1$
b. $m\angle3 = 65^{\circ}$, Reason: Vertical - angle with $\angle1$
c. $m\angle4 = 115^{\circ}$, Reason: Vertical - angle with $\angle2$
d. $m\angle5 = 65^{\circ}$, Reason: Corresponding - angle with $\angle1$
e. $m\angle6 = 115^{\circ}$, Reason: Linear - pair with $\angle5$
f. $m\angle7 = 65^{\circ}$, Reason: Vertical - angle with $\angle5$
g. $m\angle8 = 115^{\circ}$, Reason: Vertical - angle with $\angle6$