Question

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

Answer 1

Answer:

66°

Step-by-step 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

$\angle NOP+\angle MPO+\angle MNO+\angle NMP=360^{\circ}\\ \\114^{\circ}+90^{\circ}+90^{\circ}+x^{\circ}=360^{\circ}\\ \\x^{\circ}=360^{\circ}-114^{\circ}-90^{\circ}-90^{\circ}\\ \\x^{\circ}=66^{\circ}$

Answer 2

Answer:

The value of x = 66°

Step-by-step 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°