In the below figure $A B, C D$ and $E F$ are three lines concurrent at $O$ . Find the value of $y$ .

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Solution

In the given figure,

$∠ B O F = 5 y$

So,
$∠ E O A = ∠ B O F = 5 y$ ( vertically opposite angles )

Also
$∠ C O E + ∠ E O A + ∠ A O D = 180^{\circ}$ ( supplementary angles )

$2 y + 5 y + 2 y = 180^{\circ}$

$9 y = 180^{\circ}$

$y = \frac{180}{9} = 20^{\circ}$

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In the given figure, three coplanar lines AB, CD, and EF intersect at point O. Find the values of x, y, z, and t.

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In the adjoining figure, three coplanar lines AB, CD and EF intersect at a point O, forming angles as shown. Find the values of x,y,z and t.

\leftarrow \to A B, \leftarrow \to C D

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x : y : z = 2 : 3 : 5

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