.In each case; given below, find the value of x in terms of a, b and c.

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b + a - c

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b - a - c

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a - c - b

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a - c + b

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Solution

The correct option is B x $=$ b - a - c
Join BD
In $△ B D C$ ,
$∠ C D B + ∠ B C D + ∠ C B D = 180$ (Sum of angles of triangle)
$∠ C D B + ∠ C B D + b = 180$
$∠ C D B + ∠ C B D = 180 - b$
Now in $△ A B D$
$∠ B A D + ∠ A D B + ∠ A B D = 180$ (Sum of angles of triangle)
$∠ B A D + ∠ A D C + ∠ C D B + ∠ A B C + ∠ C B D = 180$
$a + x + ∠ C D B + ∠ C B D + c = 180$
$a + x + 180 - b + c = 180$
$x = b - a - c$

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