in the given figure 2b-a=65 degree and angle boc = 90 degree find the measure of angle AOB , AOD and COD
Answers
Answer:
∠AOB = 50°
∠AOD = 70°
∠COD = 150°
Step-by-step explanation:
Sum of all the angles around point O will be 360°
∴ ∠AOB + ∠BOC + ∠COD + ∠DOA = 360°
⇒ a + 90° + (2a + b + 15°) + 2b = 360°
⇒ 3a + 3b = 360° - 105°
⇒ a + b = 85° ....................... (1)
Also given
2a - b = 65° ......................... (2)
Adding eq (1) and eq (2)
3a = 150°
⇒ a = 50°
Putting the value of a in eq (1)
we get b = 35°
Therefore
∠AOB = a = 50°
∠AOD = 2b = 2 × 35° = 70°
∠COD = 2a + b + 15° = 2 × 50° + 35° + 15° = 150°
Answer:
∠AOB = 50°
∠AOD = 70°
∠COD = 150°
Step-by-step explanation:
Sum of all the angles around point O will be 360°
∴ ∠AOB + ∠BOC + ∠COD + ∠DOA = 360°
⇒ a + 90° + (2a + b + 15°) + 2b = 360°
⇒ 3a + 3b = 360° - 105°
⇒ a + b = 85° ....................... (1)
Also given
2a - b = 65° ......................... (2)
Adding eq (1) and eq (2)
3a = 150°
⇒ a = 50°
Putting the value of a in eq (1)
we get b = 35°
Therefore
∠AOB = a = 50°
∠AOD = 2b = 2 × 35° = 70°
∠COD = 2a + b + 15° = 2 × 50° + 35° + 15° = 150°