Question

Find mDCAˆ. the question says that the angle is 3x+19 the smaller arc is 91 and the bigger is 17x-3 it is one of those problems were the difference in the arcs divided by two equals the angle

Answer 1

Answer: Option C.

Step-by-step explanation:

Let as consider the below figure is attached below.

We know that angle between tangent and secant is half of difference of major and minor arcs.

$\angle ABC=\dfrac{arc(AD)-arc(AC)}{2}$

$3x+19=\dfrac{17x-3-91}{2}$

Multiply both sides by 2.

$6x+38=17x-94$

$38+94=17x-6x$

$132=11x$

Divide both sides by 11.

$12=x$

The value of x is 12.

$arc(AD)=17(12)-3$

$arc(AD)=204-3$

$arc(AD)=201^{\circ}$

Now,

$arc(DCA)=360^\circ-arc(AD)$

$arc(DCA)=360^\circ-201^{\circ}$

$m\widehat {DCA}=159^{\circ}$

Therefore, the correct option is C .