Question

21. In the given figure, 2b-a = 65° and ZBOC = 90°, find the measure of ZAOB, ZAOD and ZCOD. с B 2a+b+15 А 26°​

Answer 1

Answer:

ZAOB = 50°

ZAOD = 70°

ZCOD = 150°

Step-by-step explanation:

Sum of all the angles around point O will be 360°

.. ZAOB + ZBOC + <COD + 2DOA = 360°

⇒ a + 90° + (2a + b + 15°) + 2b = 360°

→ 3a + 3b = 360° - 105°

⇒ a + b = 85°

Also given

2a - b = 65°

Adding eq (1) and eq (2)

3a = 150°

⇒ a = 50°

Putting the value of a in eq (1)

we get b = 35°

Therefore

ZAOB = a = 50°

ZAOD = 2b = 2 x 35° = 70°

ZCOD = 2a + b + 15° = 2 x 50° + 35° +15° =

150°