By using cosine formula of triangles we got that measure of ∠C is 25.94 °
What is a quadrilateral ?
Quadrilateral is a closed shape with 4 sides and 4 corners.
Here given that
AB=5.8 cm
BC=5.4 cm
CD=3.3 cm
AD=6.2 cm
and [tex]\angle A=27[/tex] °
in [tex]\triangle \mathrm{ABD}[/tex]
Applying cosine formula
[tex]$\begin{aligned}&\mathrm{BD}^{2}=\mathrm{AB}^{2}+A D^{2}-2(\mathrm{AB})(\mathrm{BD}) \cos A \\\\&\mathrm{BD}^{2}=(5.8)^{2}+(6.2)^{2}-2(5.8)(6.2)\left(\cos 27^{\circ}\right) \\\\&\mathrm{BD}^{2}=33.64+38.44-64.08\\ \\&\mathrm{BD}^{2}=8 \\\\&\mathrm{BD}=\sqrt{8}\end{aligned}$[/tex]
Now in [tex]\triangle B C D[/tex]
Applying cosine formula
[tex]$\begin{aligned}&\mathrm{BD}^{2}=\mathrm{BC}^{2}+\mathrm{CD}^{2}-2(\mathrm{BC})(\mathrm{CD}) \cos \mathrm{C} \\\\&(\sqrt{8})^{2}=(5.4)^{2}+(3.3)^{2}-2(5.4)(3.3) \cos \mathrm{C} \\\\&8=29.16+10.89-35.64 \cos \mathrm{C}\\ \\&35.64 \cos \mathrm{C}=32.05\\ \\&\cos \mathrm{C}=0.89927 \\\\&\mathrm{C}=\cos ^{-1}(0.89927) \\&\end{aligned}$[/tex]
C=25.94 °
By using cosine formula of triangles we got that measure of ∠C is 25.94 °
To know more about Quadrilateral visit :https://brainly.com/question/4611638
