Question

find the missing angles. the measure of angle 3 is 56 and the measure of angle 6 is 40. the measure of angle 1 is type your answer... the measure of angle 2 is type your answer... the measure of angle 4 is type your answer...

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle 1 and angle 6 are vertical angles. Since $\angle6 = 40^{\circ}$, then $\angle1=40^{\circ}$.

Step2: Use linear - pair property for $\angle2$

$\angle2$ and $\angle3$ form a linear pair. A linear pair of angles sums to $180^{\circ}$. Given $\angle3 = 56^{\circ}$, then $\angle2=180 - 56=124^{\circ}$.

Step3: Use vertical - angle property for $\angle4$

$\angle4$ and $\angle2$ are vertical angles. Since $\angle2 = 124^{\circ}$, then $\angle4 = 124^{\circ}$.

Answer:

The measure of angle 1 is $40^{\circ}$.
The measure of angle 2 is $124^{\circ}$.
The measure of angle 4 is $124^{\circ}$.