Question

if m∠6 = 142°, find each measure. give you a. m∠1 = b. m∠2 = c. m∠3 = d. m∠4 = e. m∠5 = f. m∠7 = g. m∠8 =

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle6$ and $\angle2$ are vertical angles. So $m\angle2 = m\angle6=142^{\circ}$.

Step2: Identify linear - pair relationship

$\angle1$ and $\angle2$ form a linear - pair. Since the sum of angles in a linear - pair is $180^{\circ}$, $m\angle1=180 - m\angle2=180 - 142 = 38^{\circ}$.

Step3: Use vertical - angle relationship again

$\angle1$ and $\angle3$ are vertical angles, so $m\angle3 = m\angle1 = 38^{\circ}$.

Step4: Use linear - pair relationship

$\angle3$ and $\angle4$ form a linear - pair, so $m\angle4=180 - m\angle3=180 - 38 = 142^{\circ}$.

Step5: Use corresponding - angle relationship

Assume the lines are parallel. $\angle6$ and $\angle5$ are corresponding angles, so $m\angle5 = m\angle6=142^{\circ}$.

Step6: Use vertical - angle relationship

$\angle6$ and $\angle8$ are vertical angles, so $m\angle8 = m\angle6=142^{\circ}$.

Step7: Use vertical - angle relationship

$\angle7$ and $\angle5$ are vertical angles, so $m\angle7 = m\angle5=142^{\circ}$.

Answer:

a. $m\angle1 = 38^{\circ}$
b. $m\angle2 = 142^{\circ}$
c. $m\angle3 = 38^{\circ}$
d. $m\angle4 = 142^{\circ}$
e. $m\angle5 = 142^{\circ}$
f. $m\angle7 = 142^{\circ}$
g. $m\angle8 = 142^{\circ}$