Question

If arc mDC equals 4x - 2 the arc mBC is equal to 20° and angle A measures 12°. Find the value of x.

Answer 1

The answe is -24 Bc isf the negative number i

Answer 2

The value of x is 11.5.

Explanation:

Since, when one tangent and one secant intersect outside a circle, then the measure of the intersection angle is half of the difference of the intercepted arcs,

In the given diagram,

AD is the secant and AC is the tangent of the circle,

Also, AD and AC intersect at A,

Thus, by the above statement,

`m\angle A=\frac{m\widehat{DC}-m\widehat{BC}}{2}`

Here,

`m\angle A=12^(\circ)`

`m\widehat{DC}=4x-2`

`m\widehat{BC}=20^(\circ)`

`\implies 12=(4x-2-20)/(2)`

`24=4x-22`

`46=4x`

`\implies x=11.5`