Question

a is parallel to b and p is a transversal. if m∠1 = 140°, find the measure of each angle. m∠2 = ____ 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. So $m\angle1 + m\angle2=180^{\circ}$. Given $m\angle1 = 140^{\circ}$, then $m\angle2=180^{\circ}-140^{\circ}=40^{\circ}$.

Step2: Use vertical - angle property

$\angle1$ and $\angle3$ are vertical angles. So $m\angle3 = m\angle1=140^{\circ}$.

Step3: Use vertical - angle property

$\angle2$ and $\angle4$ are vertical angles. So $m\angle4 = m\angle2 = 40^{\circ}$.

Step4: Use corresponding - angle property

$\angle1$ and $\angle5$ are corresponding angles. Since $a\parallel b$, $m\angle5 = m\angle1=140^{\circ}$.

Step5: Use vertical - angle property

$\angle5$ and $\angle7$ are vertical angles. So $m\angle7 = m\angle5=140^{\circ}$.

Step6: Use vertical - angle property

$\angle6$ and $\angle8$ are vertical angles. Also, $\angle2$ and $\angle6$ are corresponding angles. So $m\angle6 = m\angle2 = 40^{\circ}$ and $m\angle8 = m\angle6=40^{\circ}$.

Answer:

$m\angle2 = 40^{\circ}$
$m\angle3 = 140^{\circ}$
$m\angle4 = 40^{\circ}$
$m\angle5 = 140^{\circ}$
$m\angle6 = 40^{\circ}$
$m\angle7 = 140^{\circ}$
$m\angle8 = 40^{\circ}$