Question

in the diagram below, AB and BC are tangent to O. Which equation could be solved to find y, the measure of ADC

Answer 1

Answer:

A

Step-by-step explanation:

∠ABC is formed by 2 tangents to the circle and is measured as

∠ABC = $\frac{1}{2}$ (m  arc ADC - m arc AC ), that is

$\frac{1}{2}$ (y - 119) = 61 → A

Answer 2

Answer:

A. $\frac{1}{2}(y^{\circ}-119^{\circ})=61^{\circ}$

Step-by-step explanation:

We have been given a diagram. We are asked to choose the equation that can be used to solve for y.

We know that measure formed by two intersecting tangents outside a circle is half the difference of corresponding arcs.

$m\angle ABC=\frac{1}{2}(\widehat{ADC}-\widehat{AC})$

$61^{\circ}=\frac{1}{2}(y^{\circ}-119^{\circ})$

Switch sides:

$\frac{1}{2}(y^{\circ}-119^{\circ})=61^{\circ}$

Therefore, option A is the correct choice.