Question

Triangle XYZ is inscribed inside a cirlce with diameter XZ and the inscribed angle at Y. The measure at X is 59 degrees. using what you know about inscribed angles,find the arc measure of XY

Answer 1

who told you XYZ is isosceles?

Answer 2

Since triangle XYZ is inscribed in the circle, we know that the measure of angle Y is equal to half the measure of its intercepted arc, which we will call arc XY.

Arc XY = 2 * angle Y

Since angle X is 59 degrees, we know that angle Y is also 59 degrees, as triangle XYZ is an isosceles triangle.

Therefore, arc XY = 2 * 59 = 118 degrees.

Answer 3

I apologize for the mistake. Given that triangle XYZ is an inscribed triangle, we can instead apply the inscribed angle theorem which states that the measure of an inscribed angle is equal to half the measure of its intercepted arc.

Since angle X is 59 degrees, the measure of arc XY can be calculated as:

arc XY = 2 * angle X
arc XY = 2 * 59
arc XY = 118 degrees

Therefore, the measure of arc XY is 118 degrees. Thank you for pointing out the error.