find value of x
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Given : Pantagonal figure in attachment
To find : Value of angle x
Solution :
We will solve this question by using the concept of angle sum property of pantagon. We know that sum of all interior angles of pantagon is 540°. Firstly we will try to find other interior angles of pantagon to find the value of x.
Finding angle AED :
∠ AED + 70° = 180° ( linear pair )
∠ AED = 180° - 70°
∠ AED = 110°
Finding angle ABC :
∠ ABC + 60° = 180° ( Linear pair )
∠ ABC = 180° - 60°
∠ ABC = 120°
Finding angle EAB :
∠ EAB + 90° = 180° ( linear pair )
∠ EAB = 180° - 90°
∠ EAB = 90°
Finding angle EDC :
∠ EAB + ∠ ABC + ∠ AED + ∠ EDC + ∠ BCD = 540° ( Angle sum property of pantagon )
90° + 120° + 110° + ∠ EDC + 90° = 540°
∠ EDC + 410° = 540°
∠ EDC = 540° - 410°
∠ EDC = 130°
Finding angle x :
x + ∠ EDC = 180° ( Linear pair )
x + 130° = 180°
x = 180° - 130°
x = 50°
So the required angle x is 50°.
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