Question

If ABCD is a cyclic quadrilateral
whose angles
are as marked.
Find all four angles.​

Answer 1

Answer:

108° , 72°, 80° and 100° .

Step-by-step explanation:

ABCD is a cyclic quadrilateral.

So, the sum of the opposite angles is always 180°.

Therefore,

3x + 2x = 180°.

5x = 180°.

x = 180°/ 5 .

x = 36.

3x = 3 × 36

3x = 108°

2x = 2 × 36 .

2x = 72°

Now,

Similarly,

4y + 5y = 180° .

9y = 180° .

y = 180°/ 9 .

y = 20.

4y = 4 × 20 .

4y = 80° .

5y = 5 × 20 .

5y = 100° .

So, the angles are 108° , 72° , 80° and 100° .

Hope it helped you