in the given figure, ABCD is a square and BEC is an equilateral triangle. find angle AEB and angle DAE.
Answers
Step-by-step explanation:
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Answer:
L BEC = 15°
L DAE = 75°
Step-by-step explanation:
all interior angles of a square are = 90°
LD = L C = L DAB = L ABC = 90
all angles of equilateral triangle are = 60°
L BCE = L BEC = L EBC = 60
AB=BC=CD=CA (sides of square)
BC=BE=CE (sides of equilateral ∆)
therefore, BC = BE = AB --------------(1)
L B = L ABC + L EBC
L B = 90 + 60
L B = 150°
in ∆ABE,
L BAE + L ABC + L AEB = 180° (angles of ∆) ------(2)
(since AB = BE) from eq. (1)
L BAE = L AEB ---------(3)
so eq. (2) becomes,
L BAE + L BAE + L ABC = 180°
2L BAE + L ABC = 180
2L BAE + 150 = 180
2L BAE = 180-150 = 30
L BAE = 30/2 = 15°
L AEB = 15° (from eq. 3)
Now, L A = 90°
so, L DAE + L BAE = 90°
L DAE + 15 = 90
L DAE = 90-15
L DAE = 75°
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