Points A, D, C, B and E are concyclic. If ∠AEC = 50° and ∠ABD = 30°, then what is the measure (in degrees) of ∠CBD?

20

AD & AC are joined

Now,

\(\angle\)AEC = \({50}^\circ\) and \(\angle\)AEC = \(\angle\)ABC = \({50}^\circ\)

\(\angle\)ABD = \({30}^\circ\)

Now,

\(\angle\)ABC = \(\angle\)ABD + \(\angle\)CBD

= 50= 30 + \(\angle\)CBD

= \(\angle\)CBD = 50 -30

= \(\angle\)CBD = 20

Therefore, measure of \(\angle\)CBD is \({20}^\circ\).