Calculate the size of angle BCD.

July 8, 2026Mathematics

ScanSolve AI Answer

July 8, 2026

Answer

$\text{92}^\circ$

Step 1: Identify the known angles in the quadrilateral ABCD. From the image, we can see: • Angle A is a right angle: $\angle A = 90^\circ$ . • Angle B is given: $\angle B = 128^\circ$ . • Angle D ( $\angle ADC$ ) can be read from the protractor. The line DA aligns with $0^\circ$ and the line DC aligns with $50^\circ$ on the outer scale. So, $\angle D = 50^\circ$ .

Step 2: Use the property that the sum of interior angles in a quadrilateral is $360^\circ$ . $\angle A + \angle B + \angle BCD + \angle D = 360^\circ$

Step 3: Substitute the known angle values into the equation. $90^\circ + 128^\circ + \angle BCD + 50^\circ = 360^\circ$

Step 4: Sum the known angles. $(90^\circ + 128^\circ + 50^\circ) + \angle BCD = 360^\circ$ $268^\circ + \angle BCD = 360^\circ$

Step 5: Solve for $\angle BCD$ . $\angle BCD = 360^\circ - 268^\circ$ $\angle BCD = 92^\circ$

The size of angle BCD is $\boxed{92^\circ}$ .

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Quick Answer

Identify the known angles in the quadrilateral ABCD. From the image, we can see: • Angle A is a right angle: A = 90^.

Asked on July 8, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on July 8, 2026

Step 1: Identify the known angles in the quadrilateral ABCD. From the image, we can see: • Angle A is a right angle: A = 90^. • Angle B is given: B = 128^. • Angle D ( ADC) can be read from the protractor. The line DA aligns with 0^ and the line DC aligns with 50^ on the outer scale. So, D = 50^. Step 2: Use the property that the sum of interior angles in a quadrilateral is 360^. A + B + BCD + D = 360^ Step 3: Substitute the known angle values into the equation. 90^ + 128^ + BCD + 50^ = 360^ Step 4: Sum the known angles. (90^ + 128^ + 50^) + BCD = 360^ 268^ + BCD = 360^ Step 5: Solve for BCD. BCD = 360^ - 268^ BCD = 92^ The size of angle BCD is 92^. Send me the next one 📸