Question

if the measure of ∠1 = 132°, find the measure of all the other angles. 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. The sum of angles in a linear pair is $180^{\circ}$. So, $m\angle2=180 - m\angle1$. Substituting $m\angle1 = 132^{\circ}$, we get $m\angle2=180 - 132=48^{\circ}$.

Step2: Use vertical - angle property

$\angle1$ and $\angle4$ are vertical angles. Vertical angles are equal. So, $m\angle4=m\angle1 = 132^{\circ}$.

Step3: Use vertical - angle property

$\angle2$ and $\angle3$ are vertical angles. So, $m\angle3=m\angle2 = 48^{\circ}$.

Step4: Use corresponding - angles property

$\angle1$ and $\angle5$ are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So, $m\angle5=m\angle1 = 132^{\circ}$.

Step5: Use vertical - angle property

$\angle5$ and $\angle8$ are vertical angles. So, $m\angle8=m\angle5 = 132^{\circ}$.

Step6: Use vertical - angle property

$\angle6$ and $\angle5$ form a linear pair and $\angle6$ and $\angle7$ are vertical angles. Since $m\angle5 = 132^{\circ}$, $m\angle6=180 - 132 = 48^{\circ}$ (linear - pair property) and $m\angle7=m\angle6 = 48^{\circ}$ (vertical - angle property).

Answer:

$m\angle2 = 48^{\circ}$
$m\angle3 = 48^{\circ}$
$m\angle4 = 132^{\circ}$
$m\angle5 = 132^{\circ}$
$m\angle6 = 48^{\circ}$
$m\angle7 = 48^{\circ}$
$m\angle8 = 132^{\circ}$