Question
In the quadrilateral ABCD, AD = DC = CB, and ADC = 100∘, ABC = 130∘. Then the measure of ACB is
Answer: Option A
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A
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Ans. (a) A, B, C will lie on a circle with centre at D (as the angle subtended by the arc at the centre i.e. 260∘ is twice subtended at the circle i.e. 130∘)
In triangle DAC, ∠DAC = ∠DCA = 40∘.Let ∠ADB = 2x ⇒ ∠ACB = x, and let ∠BDC = ∠CBD = y ⇒ 2x+y = 100∘, and 2y+x = 140∘.
Hence (a) is the right answer
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