Question

the figure to the right shows two parallel lines intersected by more than one transversal. let x = 34 degrees. find the measure of angles 1, 2 and 3.

Answer 1

`\begin{gathered} m\measuredangle1=34 \\ m\measuredangle2=56 \\ m\measuredangle3=146 \end{gathered}`

Step-by-step explanation

Step 1

as the horizontal lines are parallel, the angles (1) and x are congruents, so

`\begin{gathered} m\measuredangle1=x \\ so,\text{replacing} \\ m\measuredangle1=34 \end{gathered}`

Step 2

Now, we can see that angles (1) and (2) are complementary angesl (When two angles add to 90°)

so

`\begin{gathered} m\measuredangle1+m\measuredangle2=90 \\ \text{replacing} \\ 34+m\measuredangle2=90 \\ \text{subtract 34 in boht sides} \\ -34+34+m\measuredangle2=90-34 \\ m\measuredangle2=56 \end{gathered}`

Step 3

finally, angles (1) and angle (3) are supplementary angles (Two Angles are Supplementary when they add up to 180 degrees)

so

`\begin{gathered} m\measuredangle1+m\measuredangle3=180 \\ \text{replace} \\ 34+m\measuredangle3=180 \\ to\text{ solve for x, subtract 34 in both sides} \\ -34+34+m\measuredangle3=180-34 \\ m\measuredangle3=146 \end{gathered}`

i hope this helps you