Question

IN FIG.6.14,lines XY and MN intersect at O.If POY=90 and a:b=2:3,find c.​

Answer 1

Answer:

HERE IS YOUR ANSWER ☝️☝️

Answer 2

$\huge\star{\orange{\underline{\tt{Explanation:}}}}$

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• We know that the sum of linear pair are always equal to $\tt{\pink{180}}$

So,

$\tt{\blue{∠POY+a+b=180}}$

Putting the value of $\tt{\blue{∠POY=90}}$ (as given in the question) we get,

$\tt{\blue{a+b =90}}$

Now, it is given that $\tt{\blue{a:b=2:3}}$ so,

$\tt{\blue{Let\:a\:be\:2x\:and\:b\:be\:3x}}$

$\tt{\blue{∴2x+3x=90}}$

Solving this we get

$\tt{\blue{5x=90}}$

So, $\tt{\blue{x=18}}$

$\tt{\blue{∴a=2×18=36}}$

Similarly b can be calculated and the value will be

$\tt{\blue{b=3×18=54}}$

From the diagram, $\tt{\blue{b+c}}$ also forms a straight angle so,

$\tt{\blue{b+c=180}}$

$\leadsto$$\tt{\blue{c+54=180}}$

$\large\leadsto$ $\large\star$$\huge\boxed{\boxed{\tt{\pink{∴c =126}}}}$