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The table shows the height of some students in a school. Calculate correct to one decimal place, the Mean, Standard deviation, and Mean deviation of the distribution.

Mathematics

ScanSolve AI Answer

Answer

70∘\text{70}^\circ

Step-by-step solution

5 steps
  1. Identify the given parallel lines and angles.

    We are given that PQ∥RSPQ \parallel RS.
    We have ∠TPQ=32∘\angle TPQ = 32^\circ and ∠TRS=38∘\angle TRS = 38^\circ.
    We need to find the value of angle gg, which is ∠PTR\angle PTR.

  2. Draw an auxiliary line through point TT parallel to PQPQ and RSRS.

    Let's draw a line XYXY passing through TT such that XY∥PQ∥RSXY \parallel PQ \parallel RS.

  3. Use the property of alternate interior angles.

    Since PQ∥XYPQ \parallel XY, the alternate interior angles are equal.
    Therefore, ∠PTX=∠TPQ=32∘\angle PTX = \angle TPQ = 32^\circ.

  4. Use the property of alternate interior angles again.

    Since RS∥XYRS \parallel XY, the alternate interior angles are equal.
    Therefore, ∠RTX=∠TRS=38∘\angle RTX = \angle TRS = 38^\circ.

  5. Calculate the angle gg.

    From the diagram, angle gg is the sum of ∠PTX\angle PTX and ∠RTX\angle RTX.

    g=∠PTX+∠RTXg = \angle PTX + \angle RTX g=32∘+38∘g = 32^\circ + 38^\circ g=70∘g = 70^\circ

    The value of the angle marked gg is 70∘\boxed{\text{70}^\circ}.

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