Question

1. if m∠3 = 153°, then what are the measures of the remaining angles? o m∠1 = 27°, m∠2 = 27°, m∠4 = 153° o m∠1 = 27°, m∠2 = 153°, m∠4 = 153° o m∠1 = 153°, m∠2 = 27°, m∠4 = 27° o m∠1 = 153°, m∠2 = 153°, m∠4 = 153°

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles, so $m\angle1=m\angle3 = 153^{\circ}$.

Step2: Identify linear - pair angles

$\angle2$ and $\angle3$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So $m\angle2=180 - m\angle3=180 - 153=27^{\circ}$.

Step3: Identify another vertical - angle

$\angle2$ and $\angle4$ are vertical angles. So $m\angle4=m\angle2 = 27^{\circ}$.

Answer:

$m\angle1 = 153^{\circ},m\angle2 = 27^{\circ},m\angle4 = 27^{\circ}$