In the given figure, $A O B$ is a diameter and $D C$ is parallel to $A B$. If $\angle C A B=x^0$; find (in terms of $x$ ) the values of: $\angle$ ADC.
Exercise 17 (A) | Q 48.4 | Page 261
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$\mathrm{DC} \| \mathrm{AO}$
$\therefore \angle \mathrm{ACD}=\angle \mathrm{OAC}=\mathrm{x} \text { (Alternate angles) }$
By angle sum property,
$\angle A D C=180^{\circ}-\angle D A C-\angle A C D$
$=180^{\circ}-\left(90^{\circ}-2 x\right)-x$
$=90^{\circ}+x$
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In the figure, given below, P and Q are the centres of two circles intersecting at B and C ACD is a straight line. Calculate the numerical value of x .
In the given figure, AB is a diameter of the circle with centre O. DO is parallel to CB and ∠DCB = 120°.
Calculate : ∠DAB
Also show that the ΔAOD is an equilateral triangle .