Question

Point O is the center of the circle. What is the value of x?

Answer 1

The value of x = 66°

Explanation:

From the figure we can see that,

PM and MN are the tangent from the point M to the circle with center O

m<PON = 114°

To find the value of x

From the figure we can write,

m<PON + m<PMN = 180°

114 + x = 180

x = 180 - 114 = 66°

Therefore the value of x = 66°

Answer 2

66°

Explanation:

Since segments MN and MP are tangent to the circle, then

`\angle MPO=\angle MNO=90^(\circ)`

The sum of the measures of all interior angles of the quadrilateral is equal to 360°, so

`\angle NOP+\angle MPO+\angle MNO+\angle NMP=360^(\circ)\\ \\114^(\circ)+90^(\circ)+90^(\circ)+x^(\circ)=360^(\circ)\\ \\x^(\circ)=360^(\circ)-114^(\circ)-90^(\circ)-90^(\circ)\\ \\x^(\circ)=66^(\circ)`