H= 20°
Explanation
as HJ is congruent to HK , here we have an isosceles triangle, The angles opposite to equal sides are equal in measure,so
Step 1
[tex]\begin{gathered} \measuredangle K=\measuredangle J \\ \measuredangle K=180-\measuredangle HKL \\ \measuredangle K=180-(x+50) \\ \measuredangle K=130-x \end{gathered}[/tex]
also, we know the sum of the internal angles in a triangle equals 180, so
[tex]\begin{gathered} \measuredangle H+\measuredangle K+\measuredangle J=180 \\ x-30+130-x+130-x=180 \\ -x+230=180 \\ \text{subtract 230 in both sides} \\ -x+230-230=180-230 \\ x=50 \end{gathered}[/tex]
Step 2
now, replace in angle H
[tex]\begin{gathered} H=x-30 \\ H=50-30 \\ H=20 \end{gathered}[/tex]
therefore, the measurement fo H is
H= 20°
I hope this helps you
