Points A, B and C are on circle with centre O such that ∠BOC = 84°. If AC is produced to a point D such that ∠BDC = 40°, then find the measure of ∠ABD (in degrees).
Answer & explanation
Correct answer: option 1
Now, \(\angle\)BAC = 84/2 = 42
So, \(\angle\)BDC = 40 = \(\angle\)BDA
So, from \(\Delta \)BAD,
\(\angle\)BAD + \(\angle\)BDA + \(\angle\)ABD = 180
= 42 + 40 + \(\angle\)ABD = 180
= \(\angle\)ABD = 180 - (42 + 40)
= \(\angle\)ABD = 98
Therefore, \(\angle\)ABD is \({98}^\circ\).