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?