In the given figure, sides of $△ P Q R$ and $Δ X Y Z$ are parallel to each other. Prove that, $∠ P Q R =$ $∠ X Y Z$ .

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Solution

A line $¯ ¯¯¯¯¯¯¯ ¯ O Q$ is drawn through $Y$
from $O$ perpendiculars are drawn to $\to Q P, \to Q R, \to Y B, \to Y Z$
in $△ O A Q & △ O B Y$
$m ∠ O A Q = m ∠ O B Y = 90 °$
$m ∠ B O Y = m ∠ A O Q$
so $m ∠ O Y B = m ∠ O Q A$ ......(1)
similarly considering $△ O C Y & △ O D Q$ we can get
$m ∠ O Y C = m ∠ O Q D$ .....(2)
from (1) & (2)
$m ∠ O Y B + m ∠ O Y C = m ∠ O Q A + m ∠ O Q D \Rightarrow m ∠ P Q R = m ∠ X Y Z$
(Hence proved)

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