Respuesta :

LammettHash

If [tex]m\widehat{BY}=40^\circ[/tex], then the central angle [tex]\angle BOY[/tex] has the same measure, and by the inscribed angle theorem we have

[tex]m\angle BAY=\dfrac12m\angle BOY=20^\circ[/tex]

It's impossible to know what the measure of angle YAC is from this information alone, but assuming AC is tangent to the circle, then angles BAY and YAC are complementary, so that [tex]m\angle YAC=70^\circ[/tex].

MrRoyal

The line AC is the tangent of the line, and the measure of the angle YAC is 70 degrees

How to determine the measure of YAC?

The measure of the arc is given as:

Arc BY = 40 degrees

The measure of angle BAY is calculated using:

BAY = 0.5 * BY

This gives

BAY = 0.5 * 40

BAY = 20

The angle at a tangent is 90 degrees.

This means that:

BAY + YAC = 90

Substitute 20 for BAY

20 + YAC = 90

Subtract 20 from both sides

YAC = 70

Hence, the measure of the angle YAC is 70 degrees

Read more about tangent lines at:

https://brainly.com/question/6617153

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