The quadrilateral ABCD is inscribed in a circle. Rays BA and CD. They intersect at points L, and rays BC

The quadrilateral ABCD is inscribed in a circle. Rays BA and CD. They intersect at points L, and rays BC and AD-at points K. Find the angle ABC, if the angle CKD = 27 °, the angle АLD = 33 °

The angle ABC of the quadrilateral ABCD is the outer angle of the triangle BCL. According to the property of the outer corners of the triangle, the angle ABC = BLC + BCL = 33 + BCL.

The angle ADC of the quadrilateral ABCD is the outer angle of the triangle CDK. According to the property of the outer corners of the triangle, the angle АDC = DCK + СKD = DCK + 27.

Angle BCL = DCK as vertical angles at the intersection of lines BK and DL.

The sum of the opposite angles of the inscribed quadrilateral is 180.

Then ABC + ADC = 180.

33 + BCL + DCK + 27 = 180.

2 * DSC = 180 – 27 – 33 = 120.

DSC = 120/2 = 60.

Let’s define the angle ABC. Angle ABC = DCK + 33 = 60 + 33 = 93.

Answer: Angle ABC is 93.