Explanation
Step 1
as the horizontal lines are parallel, the angles (1) and x are congruents, so
[tex]\begin{gathered} m\measuredangle1=x \\ so,\text{replacing} \\ m\measuredangle1=34 \end{gathered}[/tex]Step 2
Now, we can see that angles (1) and (2) are complementary angesl (When two angles add to 90°)
so
[tex]\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}[/tex]Step 3
finally, angles (1) and angle (3) are supplementary angles (Two Angles are Supplementary when they add up to 180 degrees)
so
[tex]\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}[/tex]i hope this helps you
