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Answer 1

Answer:

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Answer 2

$\huge{ \underline{ \overline{\star{\sf {\red{solution}{ \star}}}}}}$

In the given figure , AB || CD , angle APQ= 50°

and angle PRD = 127°

$\angle \: apq \: + \angle \: pqc = 180 \degree \: (pair \: of \: consecutive \: interior \: angles \: are \: supplementary)$

$= 50 \degree \: + \angle \: pqc = 180 \degree$

$\angle \: pqc = 130 \degree$

$\underline{now}..$

$\angle \: pqc + \angle \: pqr = 180 \degree (linear \: pair)$

$130 \degree + x = 180 \degree$

$x = 50 \degree$

$also...x + y = 127 \degree (exterior \: angle \: of \: \triangle \: is \: equal \: to \: the \: sum \: of \: two \: interior \: opposite \: angles)$

$50 \degree + y = 127 \degree$

$y = 77 \degree$

$\underline{hence}$

$x = 50 \degree \: and \: y = 77 \degree$