Question

in the given figure find the angle measure x.​

Answer 1

Answer:

x = 105°

Step-by-step explanation:

∠GCD = 90°

∠HDA = 50°

∠EAB = 115°

∠CBF = x°

∠BCD = ∠BCD + ∠GCD = 180° [ Linear pair ( LP ) ]

           = ∠BCD + 90° = 180°

           = ∠BCD = 180° - 90°

           = ∠BCD = 90°

∠CDA = ∠CDA + ∠HDA = 180° [ Linear pair ( LP ) ]

           = ∠CDA + 50° = 180°

           = ∠CDA = 180° - 50°

           = ∠CDA = 130°

∠DAB = ∠DAB + ∠EAB = 180°

          = ∠DAB + 115° = 180°

          = ∠DAB = 180° - 115°

          = ∠DAB = 65°

∠ABC = ∠BCD + ∠CDA + ∠DAB + ∠ABC = 360° ( Angle sum property of a

                                                                                 quadrilateral )

∠ABC = 90° + 130° + 65° + ∠ABC = 360°

          = 285° + ∠ABC = 360°

          = ∠ABC = 360 - 285

          = ∠ABC = 75°

∠ABC + x = 180° [ Linear pair ( LP ) ]

75° + x = 180°

x = 180 - 75

x = 105°

∴ x = 105°