We are given a diagram showing â–³KLM and its midsegments JH, JP, and PH. Let's find the value of x.
Since ∠LHM is a straight angle, and we already know the measures of ∠MHP and ∠JHL. We can calculate the measure of ∠PHJ by using the Angle Addition Postulate.
The Triangle Midsegment Theorem tells us that if a segment joins the midpoints of two sides of a triangle, then not only is it parallel to the third side of the triangle, but also its length is half the length of that side. Since P, J, and H are the midpoints of the sides of the triangle, 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 PH and KL, then ∠PHJ and ∠LJH are congruent angles.
Let's use this information to find x.
m∠PHJ = m∠LJH
⇕
60 ° = x °
Therefore, we found that x=60.
