Answer:
Angle 1 = 35 degrees
Angle 2 = 55 degrees
Angle 3 = 145 degrees
Explanation:
We are given the figure of 2 parallel lines with transversals
[tex]x=35^{\circ}[/tex]
We will proceed to obtain angles 1, 2 & 3 as shown below:
[tex]\begin{gathered} m\angle1=35^{\circ}(corresponding\text{ }angles) \\ \\ Angles\text{ 1 \& 2 are complementary angles \lparen they sum up to 90 degrees\rparen} \\ m\angle1+m\angle2=90^{\circ} \\ 35+m\angle2=90 \\ \text{Subtract ''35''}from\text{ both sides, we have:} \\ m\angle2=90-35 \\ m\angle2=55^{\circ} \\ \\ Angles\text{ 1}\operatorname{\&}\text{ 3 are supplementary angles \lparen they sum up to 180degrees\rparen} \\ m\angle1+m\angle3=180^{\circ} \\ 35+m\angle3=180 \\ \text{Subtract ''35'' from sides, we have:} \\ m\angle3=180-35 \\ m\angle3=145^{\circ} \end{gathered}[/tex]
