Question

Determine the measure of ∠NOP.
A) 15°
B) 20°
C) 40°
D) 50°

Answer 1

The greatest answer on the test is 20

Answer 2

The correct option is B.

Explanation:

Let the center of the circle is E, and the line ON intersect the circle at A and D. The line OP intersect the circle at B and C.

Let the measure of ∠NOP be x.

Draw line segments AC, BD, AE, BE, CE and DE.

`\angle AEB=30^(\circ)`

`\angle CED=70^(\circ)`

According to the central angle theorem, the angle inscribed on the circle from the angle two point on the circle is half of its central angle.

By using central angle theorem,

`\angle CAD=(\angle CED)/(2)=(70)/(2)=35^(\circ)`

`\angle ACB=(\angle AEB)/(2)=(30)/(2)=15^(\circ)`

According to the exterior angle theorem, the sum of two interior angles of a triangle is equal to the exterior angle of third vertex.

By using exterior angle property of a triangle,

`\angle NOP+\angle ACB=\angle CAD`

`x+15^(\circ)=35^(\circ)`

Subtract both sides by 15.

`x=35^(\circ)-15^(\circ)`

`x=20^(\circ)`

The measure of ∠NOP is 15 degree. Therefore option B is correct.