At jefferson middle school, eighty-two students were asked which sports they plan to participate in for the coming year. twenty students plan to participate in track and cross country; six students in cross country and basketball; and eight students in track and basketball. twelve students plan to participate in all three sports. a total of thirty students plan to participate in basketball, and a total of forty students plan to participate in cross country. ten students don't plan to participate in any of the three sports. how many students plan to just participate in track? 40 60 20 30

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step-by-step explanation:

i don't know

step-by-step explanation:

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.