Question

1. if m∠3 = 135°, then what are the measures of the remaining angles?

o m∠1 = 25°, m∠2 = 135°, m∠4 = 25°
o m∠1 = 25°, m∠2 = 55°, m∠4 = 25°
o m∠1 = 225°, m∠2 = 135°, m∠3 = 225°
o m∠1 = 45°, m∠2 = 135°, m∠4 = 45°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles, and $\angle2$ and $\angle4$ are vertical angles. Since $m\angle3 = 135^{\circ}$, then $m\angle1=m\angle3 = 135^{\circ}$.

Step2: Use linear - pair property

$\angle1$ and $\angle2$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So $m\angle2=180^{\circ}-m\angle1$. Substituting $m\angle1 = 135^{\circ}$, we get $m\angle2 = 180 - 135=45^{\circ}$. Since $\angle2$ and $\angle4$ are vertical angles, $m\angle4=m\angle2 = 45^{\circ}$.

Answer:

$m\angle1 = 135^{\circ},m\angle2 = 45^{\circ},m\angle4 = 45^{\circ}$ (The correct option is the last one: $m\angle1 = 45^{\circ},m\angle2 = 135^{\circ},m\angle4 = 45^{\circ}$ considering the order of the options in the multiple - choice question)