Answer:
1. DC = AB = 4 ft
2. BD = 10.80 ft
3. m<CED = [tex]90^{0}[/tex]
4. m<EBC = [tex]65^{o}[/tex]
Step-by-step explanation:
From the given quadrilateral,
Given: AB = 4 ft, AD = 10 ft and m<BAE = 65.
1. DC = AB = 4 ft (opposite sides of a parallelogram are equal)
2. Applying the Pythagoras theorem to ΔABD, we have;
[tex]/hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
[tex]BD^{2}[/tex] = [tex]4^{2}[/tex] + [tex]10^{2}[/tex]
= 16 + 100
= 116
BD = [tex]\sqrt{116}[/tex]
= 10.7703
BD = 10.80 ft
3. m<CED = [tex]90^{0}[/tex] (the diagonals bisects each other at right angle)
4. m<ABC + m<BAC + m<ACB = 180
90 + 65 + m<ACB = 180
m<ACB = 180 - 155
m<ACB = [tex]25^{0}[/tex]
So that,
m<BEC + m<EBC + m<ECB = 180
90 + m<EBC + 25 = 180
m<EBC = 180 - 115
m<EBC = [tex]65^{o}[/tex]
