Question

HJ congruent to HK measurements of angle HKL = (x+50), measurements of H = (x-30). Find the measurement of H.

Answer 1

H= 20°

Step-by-step 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

`\begin{gathered} \measuredangle K=\measuredangle J \\ \measuredangle K=180-\measuredangle HKL \\ \measuredangle K=180-(x+50) \\ \measuredangle K=130-x \end{gathered}`

also, we know the sum of the internal angles in a triangle equals 180, so

`\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}`

Step 2

now, replace in angle H

`\begin{gathered} H=x-30 \\ H=50-30 \\ H=20 \end{gathered}`

therefore, the measurement fo H is

H= 20°

I hope this helps you