We are given a diagram showing △KLM and its midsegments JH, JP, and PH. Let's find the value of x.
The Triangle Midsegment Theorem tells us that if a segment joins the midpoints of two sides of a triangle, then it is parallel to the third side of the triangle and its length is one-half the length of that side. Looking at the graph, we can note some parallel segments.
JP ∥ LM
JH ∥ KM
PH ∥ KL
According to the Alternate Interior Angles Theorem, since JH cuts the parallel segments JP and LM, then ∠ PJH and ∠ LHJ are congruent angles. Let's use this information to find x.
m∠ PJH = m∠ LHJ
⇕
57 ° = x °
Therefore, we found that x=57.
