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°.
