Question

In ΔRST (See figure), what is the value of x?

Options

• 40°

• 90°

• 80°

• 100°

Answer 1

In the given problem, we need to find the value of x.

Here, according to the corollary, “if bisectors of ∠ABC and ∠ACBof a ΔABC meet at a point O, then ∠BOC = 90° + 1/2 ∠A

In ΔRST

   `∠ROT = 90° + 1/2 ∠S`

   `∠ROT = 90° + 1/2 (x)`

        `140° = 90° + 1/2 (x)`

`140° - 90° = 1/2 (x)`

Further solving for x, we get,

`50 = 1/2 (x)`

x = 2(50°)

x = 100°

Thus, x = 100°