Question

In Δ RST (See Fig. 9.51), what is value of x ?
A. 40
B. 90°
C. 80°
D. 100

Answer 1

The value of x is 100°

Step-by-step explanation:

• Here triangle Δ RST is given

        Let angle bisector of base of triangle meet at point O. Then

        ∠ROT =140°

• Consider triangle Δ ROT and use triangle angle property

        ∠ORT +∠RTO +∠TOR =180°

        a + b + 140° =180°

        So

        a +b = 40°            ...1)

• Now consider triangle Δ RST and use triangle angle property

        ∠RST +∠STR +∠TRS =180°

        x + 2b + 2a = 180°

        x + 2(a+b) = 180°      ...2)

• From equation 1) and equation 2)

        x + 2 ×40° = 180°

        x + 80° = 180°

        x = 180° - 80°

        So

       x = 100°       Answer

Answer 2

The value of x is D. 100°

Step-by-step explanation:

In ΔROT, we have,

∠ROT + ∠RTO + ∠TRO = 180°

140° + b + a = 180°

a + b = 40° → (equation 1)

In ΔRST, we have,

∠RST + ∠SRT + ∠STR = 180°

x + a + a + b + b = 180°

x + 2 (a + b) = 180°

x + 80° = 180°

x = 180° - 80°

∴ x = 100°