Question

if the measure of ∠2 = 70°, find the measure of all the other angles.
m∠1=

m∠3=

m∠4=

m∠5=

m∠6=

m∠7=

m∠8=

Explanation:

Step1: Use linear - pair property

$\angle1$ and $\angle2$ form a linear - pair. Since the sum of angles in a linear - pair is $180^{\circ}$, and $m\angle2 = 70^{\circ}$, then $m\angle1=180 - 70=110^{\circ}$.

Step2: Use vertical - angle property

$\angle1$ and $\angle3$ are vertical angles. Vertical angles are equal, so $m\angle3 = m\angle1 = 110^{\circ}$.

Step3: Use vertical - angle property

$\angle2$ and $\angle4$ are vertical angles. Vertical angles are equal, so $m\angle4 = m\angle2 = 70^{\circ}$.

Step4: Use corresponding - angle property

$\angle2$ and $\angle6$ are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal, so $m\angle6 = m\angle2 = 70^{\circ}$.

Step5: Use linear - pair property

$\angle5$ and $\angle6$ form a linear - pair. So $m\angle5=180 - 70 = 110^{\circ}$.

Step6: Use vertical - angle property

$\angle5$ and $\angle7$ are vertical angles, so $m\angle7 = m\angle5 = 110^{\circ}$.

Step7: Use vertical - angle property

$\angle6$ and $\angle8$ are vertical angles, so $m\angle8 = m\angle6 = 70^{\circ}$.

Answer:

$m\angle1 = 110^{\circ}$
$m\angle3 = 110^{\circ}$
$m\angle4 = 70^{\circ}$
$m\angle5 = 110^{\circ}$
$m\angle6 = 70^{\circ}$
$m\angle7 = 110^{\circ}$
$m\angle8 = 70^{\circ}$