Answer:∠ CDA = 32.3°Step-by-step explanation:See the given figure attached to this answer.
Draw perpendiculars from B and C on AD which is BE and CF.
Now, Δ ABE is a right triangle and AE² = AB² - BE² = 7.5² - 6² = 20.25
⇒ AE = 4.5 cm
Now, DF = AD - EF - AE = 24 - 10 - 4.5 = 9.5 cm {Since BC = EF}
And CF = BE = 6 cm.
Now, Δ CFD is a right triangle and
[tex]\tan \beta =\frac{CF}{FD} = \frac{6}{9.5} = 0.6315[/tex] {Where β = ∠ CDA}
⇒ [tex]\beta = \tan^{-1} (0.6315)=32.27[/tex] Degree.
So, ∠ CDA = 32.3° {Correct to one decimal place} (Answer)