Points A, D, C, B and E are concyclic. If ∠AEC = 50° and ∠ABD = 30°, then what is the measure (in degrees) of ∠CBD?
Answer & explanation
Correct answer: option 1
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 \({20}^\circ\).