Consider the quadrilateral shown below that has vertices A, B, C, and D. Suppose we know the following measurements:
¯¯¯¯¯¯¯¯AB=5.8 cm
¯¯¯¯¯¯¯¯BC=5.4 cm
¯¯¯¯¯¯¯¯¯CD=3.3 cm
¯¯¯¯¯¯¯¯¯AD=6.2 cm
m∠A=27∘
What is the degree measure of ∠C?
m∠C=  °
​

C = 25.94°

Step-by-step explanation:

By applying cosine rule in ΔABD,

BD² = AB² + AD² - 2(AB)(BD)cosA

BD² = (5.8)² + (6.2)² - 2(5.8)(6.2)(cos27°)

BD² = 33.64 + 38.44 - 64.08

BD² = 8

BD = √8

By applying cosine rule in ΔBCD,

BD² = BC² + CD²- 2(BC)(CD)cosC

(√8)² = (5.4)²+ (3.3)² - 2(5.4)(3.3)cosC

8 = 29.16 + 10.89 - 35.64cosC

35.64cosC = 32.05

cosC = 0.89927

C =

C = 25.94°