Question

ABCD is a cyclic quadrilateral where BC is diameter and angle ADC = 130 degree . Find the value of angle ACB?

Answer 1

`angleACB=40^@`

Explanation:

Given : `ABCD` lie on a circle, `angleADC=130^@, and BC` is the diameter.
We know that opposite angles in a cyclic quadrilateral add up to `180^@`,
`=> angleADC+angleABC=180^@`
`=> angleABC=180-angleADC=180-130=50^@`
As `BC` is the diameter,
`=> angleBAC=90^@`,
`=> angleACB=180-(angleABC+angleBAC)=180-(50+90)=40^@`

Alternatively, you can do it this way:
As `BC=` diameter, `BDC=90^@`,
`=> angleBDA=130-90=40^@`
`=>angleACB=angleBDA=40^@`