Question

In circle NN, m, arc, M, O, equals, 66, degreesm
MO
⌢
=66
∘
. Solve for xx if m, angle, M, N, O, equals, left bracket, 5, x, plus, 38, right bracket, degreesm∠MNO=(5x+38)
∘
. If necessary, round your answer to the nearest tenth.

Answer 1

To solve for x, we need to use the property that the measure of an angle formed by two secants, tangents, or chords intersecting in the circle is equal to half the sum of the measures of the intercepted arcs.

So, we have:

m∠MNO = 1/2 * (m arc MO + m arc MN)
5x + 38 = 1/2 * (66 + m arc MN)
5x + 38 = 33 + 1/2 * m arc MN
5x = -5 + ½ m arc MN
5x = -5 + ½ (360 - arc MO)
5x = -5 + 180 - 33
5x = 142
x = 28.4

Therefore, x is approximately 28.4.