Answer :
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°
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°
