Geometry Question

Question

Quadrilateral MNOP is inscribed in Circle C such that the angle measure of P=(2x) degrees and the measure of angle N=(2x-12) degrees. What is the measure of arcMNO?

196 degrees

48 degrees

94 degrees

96 degrees

192 degrees

Answer 1

Question: Quadrilateral MNOP is inscribed in Circle C such that the angle measure of P=(2x) degrees and the measure of angle N=(2x-12) degrees. What is the measure of arcMNO?

Answer: We will be using circle theorems to solve this.

Step 1: FInd the value of x. An inscribed quidrilateral's opposite angles add up to 180 degrees. Angle P and angle N are opposite angles so the measure of those angles should add up to 180 degrees.

measure of angle N + measure of angle P = 180

(2x-12) + (2x) = 180

2x-12+2x = 180

4x-12 = 180

+12 +12

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4x = 192

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4 4

x = 48

Step 2: Find the measure of angle P. Substitute 48 for x to solve for the angle P.

P = 2x

P = 2(48)

P = 96°

Step 3: Find arc MNO. Intercepted arc is twice the measure of its inscribed angle. The inscibed angle for arc MNO is angle P. So, arc MNO is twice the measure of angle P.

arc MNO = 2*P

arc MNO = 2 (96)

arc MNO = 192°

Answer 2

Draw and label of diagram!

All four angles are inscribed and each equals one-have the subtended arc.

2x + 2x - 12 = 180°

4x = 192°

2x = 96°

MNO = 192°