the angle between two altitudes of a parallelogram through the vertex of an obtuse angle is 40.find the angles
Answers
Step-by-step explanation:
90-40=50 the angle having 50degree
The angles of parallelogram are 40°, 40°, 140° and 140°
Step-by-step explanation:
The angle between two altitudes of a parallelogram through the vertex of an obtuse angle is 40°
Please see attachment for figure.
In quadrilateral AECF
∠AEC = 90° (Altitude of quadrilateral)
∠CFA = 90° (Altitude of quadrilateral)
Sum of all angles of a quadrilateral is 360° (Angle sum property)
Therefore,
∠FAE + ∠AEC + ∠ECF + ∠CFA = 360°
∠FAE + 90° + 90° + 40° = 360°
∠FAE = 360° - 220°
∠FAE = 140°
∠A = 140° = ∠C (Opposite angle of parallelogram is equal)
∠A + ∠D = 180° (Sum adjacent angle of parallelogram is 180°)
∠D = 180° - 140°
∠D = 40°
∠D = 40° = ∠B (Opposite angle of parallelogram is equal)
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