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Question

In the figure, AB and CD are parallel lines and transversal EF intersects them at P and Q respectively. If APR=25,RQC=30 and CQF=65, then

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Solution

In the figure,

AB||CD,EF inetersects them at P and Q respectively,

APR=25,RQC=30,CQF=65

AB||CD

APQ=CQF (Corresponding angles)

y+25=65

y=6525=40

and APQ+PQC=180

(Co -interior angles)

y+25+1+30=180

40+25+1+30=180

1+95=180

1+18095=85

Now ,

ΔPQR,

RPQ+PQR+PRQ=180

(Sum of angles of a triangle )

40+x+85=180

125+x=180x=180125=55

x=55,y=40


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