ABCD is a cyclic quadrilateral such that ∠ ADB =30° and ∠ DCA =80°, then ∠ DAB =

Question

ABCD is a cyclic quadrilateral such that &#x2220; ADB =30&#xB0; and &#x2220; DCA =80&#xB0;, then &#x2220; DAB =

Philoid · Accepted Answer

ABCD is a cyclic quadrilateral

∠ADB = 30°

∠DCA = 80°

∠ADB = ∠ACB = 30° (Angle on the same segment)

Now,

∠BCD = ∠ACB + ∠DCA

= 30° + 80°

= 110°

∠OAB + ∠BCD = 180°

∠OAB + 110° = 180°

∠OAB = 70°