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In fig., Ab||CD angle APQ= 50°, …

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In fig., Ab||CD angle APQ= 50°, angle PRD=127° then the value of x and y respectively

    • Posted by Pushkar Gajbhiye 2 years, 8 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Preeti Dabral 2 years, 8 months ago

    We are given that {tex}AB\parallel CD,\angle APQ = {50^\circ }{/tex} and {tex}\angle{/tex}PRD = 127°
    We need to find the value of x and y in the figure.
    {tex}\angle{/tex}APQ = x = 50° (Alternate interior angles)
    {tex}\angle{/tex}PRD = {tex}\angle{/tex}APR = 127° (Alternate interior angles)
    {tex}\angle{/tex}APR = {tex}\angle{/tex}QPR + {tex}\angle{/tex}APQ.
    127° = y + 50°
    {tex}\Rightarrow{/tex} y = 77°.
    Therefore, we can conclude that x = 55° and y = 77°
    Alternatively, 127° = y + x (because exterior angle is equal to the sum of interior opposite angles).
    so, ​​​​​​127° = y + 50°
    which gives, x = 50° and y = 77°

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