For kite ABCD, m∠C = m∠B − 40° while m∠A = m∠B − 60°. Find m∠B in degrees.

Question

Consider kite ABCD with AB ≅ AD and BC ≅ DC. For kite ABCD, m∠C = m∠B − 40°

 while m∠A = m∠B − 60°.  Find m∠B in degrees.

Answer 1

In a regular kite, where AB ≅ AD and BC ≅ DC, we also have angle B ≅ angle D. Also, being a quadrilateral, the sum of the interior angles is 360°:

m∠A + m∠B + m∠C + m∠D = 360° 

m∠B - 60° + m∠B + m∠B-40° + m∠B = 360°

4m∠B - 100° = 360°

Can you complete it from here?