The Triangle Midsegment Theorem states that
A midsegment connecting two sides of a triangle is parallel to the third side and is half as long.
Since AY divides XT and XH into two equal parts, it qualifies as a midsegment and so TH is parallel to AY and is twice its length,Thus
AY = TH / 2 = 15.2 / 2 = 7.6
Since TH is parallel to AY <XYA = <YHT = <x since they are complementary angles.
but <XYA = 90 - 35 = 55 degrees. Thus,
<x = 55 degrees
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