Answer:
DC ≈ 26.1 cm(3 significant figures)
Step-by-step explanation:
The sum of interior angles of a quadrilateral is equals to 360 degree. For a regular quadrilateral, each angle is equals to 90 degree.
BDC is a triangle and angles in a triangle sum up to 180° . Therefore, to find ∠BDC
180 - 102° + 52° = ∠BDC
180 - 154 = 26°
∠BDC = 26°
Angle ABD can be found same way since sum of interior angles in a triangle is 180°.
∠ABD = 180 - 90 - 35
∠ABD = 55°
Side BD can be find as follows
sin 35° = opposite/hypotenuse
sin 35° = 12/BD
BD sin 35° = 12
BD = 12/sin 35°
BD = 12/0.57357643635
BD = 20.9213615475
BD ≈ 21 cm
Using sine formula we can find side CD
21/sin 52° = DC/sin 102°
DC sin 52° = 21 sin 102°
DC = 21 sin 102°/sin 52°
DC = 0.97814760073 × 21/0.7880107536
DC = 20.5410996154
/0.7880107536
DC = 26.0670295696
DC ≈ 26.1 cm(3 significant figures)
