In Fig. 16.179 ABCD is a cyclic quadrilateral. If ∠ BCD =100° and ∠ ABD =70°, find ∠ ADB.

Question

In Fig. 16.179 ABCD is a cyclic quadrilateral. If &#x2220; BCD =100&#xB0; and &#x2220; ABD =70&#xB0;, find &#x2220; ADB.

Philoid · Accepted Answer

We have,

∠BCD = 100^o

∠ABD = 70^o

Therefore,

∠DAB + ∠BCD = 180^o (Opposite angles of cyclic quadrilateral)

∠DAB + 100^o = 180^o

∠DAB = 180^o – 100^o

= 80^o

In triangle DAB, by angle sum property

∠ADB + ∠DAB + ∠ABD = 180^o

∠ABD + 80^o + 70^o = 180^o

∠ABD = 30^o