Question

PLS HELP ASAP I WIL MARK BRAINLIEST

Answer 1

Answer:

$x=80^{\circ},\\y=80^{\circ}$

Step-by-step explanation:

The measure of an angle formed by a secant and a tangent outside of a circle is half of the absolute difference between the two arcs it forms. Therefore, we have the following equation:

$m\angle A=\frac{\widehat{BC}-\widehat{BD}}{2}$

Substituting given values, we get:

$20=\frac{120-x}{2},\\40=120-x,\\x=\boxed{80^{\circ}}$

Since there are 360 degrees in a circle, we can write the following equation, using $x$, to solve for $\widehat{DC}$:

$x+\widehat{DC}+120=360,\\80+\widehat{DC}+120=360,\\\widehat{DC}=\boxed{160^{\circ}}$

The value of the angle formed by a chord and a tangent is half the measure of the arc it forms. Therefore,

$y=\frac{\widehat{DC}}{2}=\frac{160}{2}=\boxed{80^{\circ}}$