Answer:
x ≈ 77°, y = 103°
Step-by-step explanation:
Using the Sine rule in Δ BCD
[tex]\frac{2.9}{sin45}[/tex] = [tex]\frac{4}{sinx}[/tex] ( cross- multiply )
2.9sinx° = 4sin45° ( divide both sides by 2.9 )
sinx° = [tex]\frac{4sin45}{2.9}[/tex] , thus
x = [tex]sin^{-1}[/tex] ([tex]\frac{4sin45}{2.9}[/tex] ) ≈ 77° ( to the nearest degree )
Since AC and DC are congruent then Δ ACD is isosceles.
Thus the base angles are congruent, that is
∠ ADC = ∠ CAD = y°
x and y are adjacent angles and supplementary, thus
x + y = 180, that is
77 + y = 180 ( subtract 77 from both sides )
y = 103°
