ABCD is a square. Triangle DEF is equilateral. Triangle ADE is isosceles with AD = AE. CDF is a straight line. Showing all your steps, calculate the size of angle AEF.
Answers
Answer:
The size of ∡AEF is 90 °
Step-by-step explanation:
Here we have
Since ∡CDF = straight line = 180 °
∡FDE = 60 ° = Internal angle of equilateral triangle
∡CDA = 90 ° = Internal angle of a square
∡ADE + ∡CDA + ∡FDE = 180 °, Sum of angles on a straight line
Therefore ∡ADE = 180 - (∡CDA + ∡FDE) = 180 ° - 150 ° = 30 °
∡DEA = ∡ADE = 30 °
∡AEF = ∡DEA + ∡DAF (Internal angle in equilateral triangle) = 30 + 60 = 90 °
The size of ∡AEF = 90 °.
Answer:
Given that ABCD is a square
AB=BC=CD=DA...................(1)
ADE is an equilateral triangle
AE=ED=DA............................(2)
from (1) and (2)
AB=AE
Now in triangle ΔABE
∠BAE=∠BAD+∠EAD
∠BAE=90
∘
+60
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⇒∠BAE=150
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AB=AE proved above
⇒∠ABE=∠AEB angles opposite to equal sides are also equal
the sum of all angles of a triangle =180
∘
⇒∠BAE+∠ABE+∠AEB=180
∘
⇒150
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+2∠AEB=180
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⇒2∠AEB=30
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⇒∠AEB=∠AEF=15
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∠y=∠EAF+∠EAF exterior angle property of a triangle ΔAEF
∠y=15
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+60
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∠y=75
∘
hope it helps you
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