In the figure below O is the center of circle ABCD fine the values of angles w, x,y, z

w = 252

x = 108

y = 54

z = 126

Step-by-step explanation:

ABCD is a cyclic quadrilateral because it has all four vertices on the circle. This means that opposite angles are supplementary since they are both inscribed angles and add up to the whole circle; we can write and solve an equation that models the situation:

<ABC + <ADC = 180

126 + y = 180

y = 54

We can see that <Z is supplementary with <ADC because together, they form a straight angle. As stated before, <ABC is also supplementary to <ADC. They both are supplements of the same angle, meaning they are congruent.

<Z = <ABC

z = 126

Now, <ADC is an inscribed angle that intercepts the same arc as the central angle <AOC. This means <AOC is exactly twice the measure of <ADC:

<AOC = 2<ADC

x = 2(54)

x = 108

Lastly, we can see reflexive angle <AOC forms a full circle with obtuse <AOC. This means they add up to 360:

w + x = 360

w + 108 = 360

w = 252

51-50

step-by-step explanation:

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