∠DAC = ∠B + ∠C
(Exterior angle prop. of a Δ ABC)
According to question,
130° = 2A + 3A

Correct Option: D

∠DAC = ∠B + ∠C
(Exterior angle prop. of a Δ ABC)
According to question,
130° = 2A + 3A
5A = 130°
A = 26°
∴ ∠B = 52°; ∠C = 78°

Let us assume 2∠A = 3∠B = 6∠C = K

Correct Option: C

Let us assume 2∠A = 3∠B = 6∠C = K

Since A, B and C are the angles of a Δ,
∴ A + B + C = 180° .......................................... (1)
According to question,
A – B = 15° ;
⇒ A = B + 15°....................................................(2)
B – C = 30°;
⇒ B = C + 30°;...................................................(3)

Correct Option: B

Since A, B and C are the angles of a Δ,
∴ A + B + C = 180° .......................................... (1)
According to question,
A – B = 15° ;
⇒ A = B + 15°....................................................(2)
B – C = 30°;
⇒ B = C + 30°;...................................................(3)
Put the value of B from equation (2) in Equation (1), we will get
∴ A = B + 15°
A = C + 30° + 15°
A = C + 45° ........................................................(4)
From a equation,
∴ A + B + C = 180°
⇒ (C + 45°) + (C + 30°) + C = 180°
⇒ 3C + 45° + 30° = 180°
⇒ 3C = 180° – 75° = 105°
⇒ C = 35° ..........................................................(5)
From equation (4)
A = C + 45°
Put the value of C from equation (5) , we will get
∴ ∠A = 35° + 45° = 80°.

As we know the formula,

Correct Option: D

As we know the formula,

Since the angles are supplementary therefore the sum of their angles will be 180 degree.

Correct Option: A

As we know that the angles are supplementary so sum of angles will be 180 degree.
Let us assume that the ratio factor is r.
According to question,
Angles are supplementary and have a ratio of 1:4.
r + 4r = 180
⇒ 5r = 180
⇒ r = 180/5
⇒ r = 36