Question

In the quadrilateral ABCD, AD = DC = CB, and ADC = 100${}^{\circ }$, ABC = 130${}^{\circ }$. Then the measure of ACB is

• A. 20
• B. 30
• C. 50
• D. cannot be determined

Answer 1

The correct option is A 20

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${}^{\circ }$ is twice subtended at the circle i.e. 130${}^{\circ }$)

In triangle DAC, $\angle$DAC = $\angle$DCA = 40${}^{\circ }$.Let $\angle$ADB = 2x $\Rightarrow$ $\angle$ACB = x, and let $\angle$BDC = $\angle$CBD = y $\Rightarrow$ 2x+y = 100${}^{\circ }$, and 2y+x = 140${}^{\circ }$.

Hence (a) is the right answer