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In the given figure, $A D$ divides $∠ B A C$ in the ratio $1 : 3$ and $A D = D B$ . Then the value of $x$ is

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45 °

90 °

115 °

75 °

answer is B.

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Detailed Solution

It is given that

A D

divides

∠ B A C

which is in the ratio of

1 : 3

.
We have to find the value of

x

.
Consider

B E

as a straight line,
So,

∠ BAC + ∠ CAE = 180 °

∠ B A C + 108 ° = 180 °

∠ B A C = 180 ° − 108 °

= 72 °

Divide

72 °

in the ratio of

1 : 3

, so that,

a + 3 a = 72 °

4 a = 72 °

a = 72 ° 4

= 18 °

∴ ∠ B A D = 18 °

and,

∠ D A C = 3 (18 °) = 54 °

Consider the triangle

A B C

, since sum of the angles of the triangle is

180 °

∠ A + ∠ B + ∠ C = 180 °

72 ° + 18 ° + x = 180 °

90 ° + x = 180 °

x = 180 ° − 90 °

= 90 °

The value of

x

90 °

.
Hence option 2) is correct.

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