What is the range of possible values for x?

The minimum value for 2x is 0

the maximum value is achieved when A, D and C are collinear and the quadrilateral ABCD becomes an isosceles triangle ABC

base AB = 52 and vertical angle 2x + 34°

For the sine law

(sin 2x)/22 = (sin ADB)/AB

(sin 34°)/30 = (sin BDC)/BC

is given that AB = BC, and sin ADC = sin BDC because they are supplementary, so from

(sin ADC)/AB = (sin BDC)/BC

it follows

(sin 2x)/22 = (sin 34°)/30

sin 2x = 22 (sin 34°)/30

2x = asin(22 (sin 34°)/30) ≈ 24.2°

x = 0.5 asin(22 (sin 34°)/30) ≈ 12.1°

0 < x < 12.1°

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