Given that ang ADB and ang BDC measure 30 deg and 40 deg respectively what will be the measure in de...........

Quantitative Aptitude ( CCS) Geometry

Given that ∠ADB and ∠BDC measure 30° and 40° respectively, what will be the measure (in degrees) of ∠ABC in the given diagram?

110

140

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Explanation:

m∠ADC = m∠ADB + m∠BDC = 30° + 40° = 70°

∴ m∠ABC = 180 – m∠ADC = 180 – 70 = 110°

(? Angles subtended by a chord at distinct points on the circumference, in alternate segments, are supplementary.
Or if we join AB, BC, CD and AD then the resulting quadrilateral is a cyclic quadrilateral.
Opposite angles of cyclic quadrilateral are supplementary angles.)