Question

In circle Y, what is m?

59°
67°
71°
118°

Answer 1

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.


`(arc \ SR+arc \ TU)/(2)=63 \\ \\ 55+arc \ TU=63*2 \\ \\55+arc \ TU=126\\\\ \ arc \ TU = 126-55=71^o`

Answer 2

`arc\ TU=71\°`

Explanation:

we know that

The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite

In this problem we have that

`63\° =(1)/(2)(arc\ SR+arc\ TU)`

we have

`arc\ SR=55\°`

substitute and solve for arc TU

`63\° =(1)/(2)(55\°+arc\ TU)`

`126\° =(55\°+arc\ TU)`

`arc\ TU=126\°-55\°=71\°`