In Fig., line CA ⊥ AB || line CR and line PR || line BD. Find ∠x, ∠y and ∠z.

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Solution

Since CA ⊥ AB,
$∴ ∠ x = 90 °$
We know that the sum of all the angles of triangle is 180°.
$In ∆ APQ, ∠ QAP + ∠ APQ + ∠ PQA = 180 ° \Rightarrow 90 ° + ∠ APQ + 20 ° = 180 ° \Rightarrow 110 ° + ∠ APQ = 180 ° \Rightarrow ∠ APQ = 180 ° - 110 ° = 70 °$
$∠$ PBC = $∠$ APQ = $70 °$ (Corresponding angles)
Since $∠ PRC + ∠ z = 180 ° (Linear pair)$
$∴ ∠ z = 180 ° - 70 ° = 110 ° [∠ APQ = ∠ PRC (Alternate interior angles)]$

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