Question

please answer this question

Answer 1

Answer:

Consider Δ ABC

We know that, according to angle sum property of a triangle,

⇒ ∠A + ∠B + ∠C = 180°

We are given that,

⇒ ∠A = 80°, ∠B = 60°, ∠C = 2x

Substituting them in the formula we get,

⇒ 80° + 60° + 2x = 180°

⇒ 140° + 2x = 180°

⇒ 2x = 180° - 140°

⇒ 2x = 40°

⇒ x = 40° / 2 = 20°

Now consider Δ DBC,

In this triangle, ∠ D + ∠ DBC + ∠ DCB = 180°.

( Due to angle sum property )

We are given with values that,

⇒ ∠ D = y°, ∠ DBC = 60/2 = 30°, ∠ DCB = x° = 20°

Substituting the values we get,

⇒ y° + 30° + 20° = 180°

⇒ y° + 50° = 180°

⇒ y = 180° - 50°

⇒ y = 130°

Hence the value of x is 20° and value of y is 130°.

Option 3 is the right answer :)

Answer 2

In the given figure we are given that :-


Angle A = 80°

Angle B = 60°

Angle C = 2x

BD and CD are angle bisectors of angle B and angle C

Solution :-

In a ∆, we know that the sum of interior angles is 180°

=> angle A + angle B + angle C = 180°

=> 80° + 60° + 2x = 180°

=> 140° + 2x = 180°

=> 2x = 180° - 140°

=> 2x = 40°

=> x = 40/2

=> x = 20°


Now, x = 20° and we are given that BD is the angle bisector of angle B

=> angle DBC = 1/2 angle ABC

=> angle DBC = 1/2 × 60°

=> angle DBC = 30°

now, again by angle sum property of a ∆, in ∆BDC,


angle DBC + angle DCB + angle BDC = 180°

=> 30° + x + y = 180°

=> 30 + 20 + y = 180°

=> 50 + y = 180°

=> y = 180 - 50

=> y = 130°


=> x = 20° and y = 130°

Hence correct option is option 3


Hope it helps dear friend ☺️✌️