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Calculate the size of angle BCD.

Mathematics

ScanSolve AI Answer

Answer

92∘\text{92}^\circ

Step-by-step solution

5 steps
  1. Identify the known angles in the quadrilateral ABCD.

    From the image, we can see:

    • Angle A is a right angle: ∠A=90∘\angle A = 90^\circ.
    • Angle B is given: ∠B=128∘\angle B = 128^\circ.
    • Angle D (∠ADC\angle ADC) can be read from the protractor. The line DA aligns with 0∘0^\circ and the line DC aligns with 50∘50^\circ on the outer scale. So, ∠D=50∘\angle D = 50^\circ.
  2. Use the property that the sum of interior angles in a quadrilateral is 360∘360^\circ.

    ∠A+∠B+∠BCD+∠D=360∘\angle A + \angle B + \angle BCD + \angle D = 360^\circ
  3. Substitute the known angle values into the equation.

    90∘+128∘+∠BCD+50∘=360∘90^\circ + 128^\circ + \angle BCD + 50^\circ = 360^\circ
  4. Sum the known angles.

    (90∘+128∘+50∘)+∠BCD=360∘(90^\circ + 128^\circ + 50^\circ) + \angle BCD = 360^\circ 268∘+∠BCD=360∘268^\circ + \angle BCD = 360^\circ
  5. Solve for ∠BCD\angle BCD.

    ∠BCD=360∘−268∘\angle BCD = 360^\circ - 268^\circ ∠BCD=92∘\angle BCD = 92^\circ

    The size of angle BCD is 92∘\text{92}^\circ.

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