- Cyclic quadrilateral has all its vertices on circle and sum of all angles is `360^o`.
- Sum of opposite angles = `180^o`.
- External angle = Opposite internal angle.
`angle` PCB = `60^o`
So, PBC + PCB = `130^0`
See its very simple question, if you know the properties of geometry.Lets try more examples
Example2: ABCD is a parallelogram and P is any point within it. If area of parallelogram is 20 units, then what will be the sum of areas of triangle PAB and PCD?
Solution: According to the question, figure will be as follows:
Properties for this question:
- Area of parallelogram = Base `times` Height.
- Area of triangle = `1/2` Base `times` altitude.
i.e. Base `times` Height = 20
⇒ b `times` h = 20
To find = Area of ( PAB +PCD)
⇒ `(1/2) b times (PY)` + `(1/2) b times (PX)` ( See Figure)
⇒`1/2` b ( PX +PY)
⇒`1/2` b h
⇒`(1/2) times 20`
Example3: ABCD is a cyclic trapezium with AB parallel DC and AB diameter of circle. If angle CAB = `30^o`, then angle ADC will be?
Solution: According to ques, figure will be as follows:
- Angle subtended by diameter is always `90^o`.
- Sum of angles of triangle = `180^o`.
- Sum of opposite angles = `180^o`
`angle` BAC = `30^o`