Question

find value of x
help ​

Answer 1

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°.