Question

if m∠1 = 65°, find each measure. encuentra cada medicion. 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

$\angle1$ and $\angle2$ form a linear - pair. Since the sum of angles in a linear - pair is $180^{\circ}$, $m\angle2=180^{\circ}-m\angle1=180 - 65=115^{\circ}$

Step3: Vertical - angles

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

Step4: Corresponding - angles

$\angle1$ and $\angle5$ are corresponding angles. If the lines are parallel, $m\angle5=m\angle1 = 65^{\circ}$

Step5: Vertical - angles

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

Step6: Linear - pair with $\angle5$

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

Step7: Vertical - angles

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

Answer:

a. $m\angle2 = 115^{\circ}$
b. $m\angle3 = 65^{\circ}$
c. $m\angle4 = 115^{\circ}$
d. $m\angle5 = 65^{\circ}$
e. $m\angle6 = 115^{\circ}$
f. $m\angle7 = 65^{\circ}$
g. $m\angle8 = 115^{\circ}$