Question

In the figure, M is a center of the circle, F is the intersection of the lines AC and BD, and E is the intersection of the lines CM and BD. The line CM is perpendicular to the line BD. If the measure of angle MBE is `32^o`, the measure of angle CFD is . ?

Answer 1

`angleCFD=119^@`

Explanation:

As `A, B, C, and D` lie on the circle, they are cyclic quadrilateral.
`=> angleABD=angleACD` as they subtends the same arc.
Given `angle MBE=32^@,`
`=> angle ABD=angleACD=angleMBE=32^@`

`angleBME=180-32-90=58^@`
`=> angleBMC=angleBME`
As `angleBMC` is twice the `angleBDC`,
`=> angleBDC=58/2=29^@`

`=> angleCFD=180-angleACD-angleBDC`
`=180-32-29=119^@`