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Wordica · Answer 1 · 2023-07-09T02:47:14+0000

Answer:

Angle 1 = 35 degrees

Angle 2 = 55 degrees

Angle 3 = 145 degrees

Step-by-step explanation:

We are given the figure of 2 parallel lines with transversals

$x=35^(\circ)$

We will proceed to obtain angles 1, 2 & 3 as shown below:

$\begin{gathered} m\angle1=35^(\circ)(corresponding\text{ }angles) \\ \\ Angles\text{ 1 \& 2 are complementary angles \lparen they sum up to 90 degrees\rparen} \\ m\angle1+m\angle2=90^(\circ) \\ 35+m\angle2=90 \\ \text{Subtract ''35''}from\text{ both sides, we have:} \\ m\angle2=90-35 \\ m\angle2=55^(\circ) \\ \\ Angles\text{ 1}\operatorname{\&}\text{ 3 are supplementary angles \lparen they sum up to 180degrees\rparen} \\ m\angle1+m\angle3=180^(\circ) \\ 35+m\angle3=180 \\ \text{Subtract ''35'' from sides, we have:} \\ m\angle3=180-35 \\ m\angle3=145^(\circ) \end{gathered}$

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