Question

in the picture, line a is parallel to line b. m∠1 = 53°. find the other 7 angle measures. ∠2 =
∠3 =
∠4 =
∠5 =
∠6 =
∠7 =
∠8 =

Explanation:

Step1: Vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles, so $m\angle3 = m\angle1=53^{\circ}$. $\angle2$ and $\angle4$ are vertical angles, and $\angle1+\angle2 = 180^{\circ}$ (linear - pair), so $m\angle2=180 - 53=127^{\circ}$, then $m\angle4 = m\angle2 = 127^{\circ}$.

Step2: Corresponding - angle property

Since $a\parallel b$, $\angle1$ and $\angle5$ are corresponding angles, so $m\angle5 = m\angle1 = 53^{\circ}$.

Step3: Vertical - angle property for $\angle5$

$\angle5$ and $\angle7$ are vertical angles, so $m\angle7 = m\angle5 = 53^{\circ}$. $\angle6$ and $\angle8$ are vertical angles, and $\angle5+\angle6 = 180^{\circ}$ (linear - pair), so $m\angle6=180 - 53 = 127^{\circ}$, then $m\angle8 = m\angle6 = 127^{\circ}$.

Answer:

$\angle2 = 127^{\circ}$
$\angle3 = 53^{\circ}$
$\angle4 = 127^{\circ}$
$\angle5 = 53^{\circ}$
$\angle6 = 127^{\circ}$
$\angle7 = 53^{\circ}$
$\angle8 = 127^{\circ}$