Question

If the figures given below are squares, find x:

Answer 1

Let the intersecting point in both squares be O

In ABCD :-

∠DOC = 80° = ∠MOB  (Vertically Opposite Angles)

∠COB + ∠DOC = 180° (Linear Pair)

 ∠COB +    80° = 180°

              ∠COB = 180° - 80°

              ∠COB = 100°

∠COB = 100° = ∠DOM (Vertically Opposite Angles)

∠ADB = y = ∠BDC (Diagonals of a Square Bisect the Angle)

   ∠ADC = ∠ADB + ∠BDC

       90° =       y    +     y

       90° = 2y

 90° ÷ 2 = y

       45° = y            or           ∠ADB = 45° = ∠BDC

∠ADB + ∠DAM + ∠AMO + ∠DOM = 360° ( Angles of quadrilateral)

45° + 90° + x + 100° = 360°

                   235 + x = 360°

                              x = 360° - 235°

                              x = 125°

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