Find the value of x in the diagram

x = 21

Step-by-step explanation:

Inscribed angle = (3x - 3)°

Intercepted arc measure = 120°

Thus:

(3x - 3)° = ½(120°) => an inscribed angle of any circle = ½ the measure of its intercepted arc.

Multiply both sides by 2

2(3x - 3) = 120

6x - 6 = 120

6x - 6 + 6 = 120 + 6

6x = 126

6x/6 = 126/6

x = 21

In a  30°-60°-90 °  triangle   the sides are in the ratio 1 : 2 : . (for the definition of measuring angles by "degrees," see topic 12.) note that the smallest side, 1, is opposite the smallest angle,30 °; while the largest side, 2, is opposite the largest angle,  90 °. (theorem 6).