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jasenka [17]
3 years ago
14

The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60°. Find t

he angles of the parallelogram
Mathematics
1 answer:
Galina-37 [17]3 years ago
7 0

Answer:

∠A = ∠C = 60°  

∠B = ∠D = 120°

Step-by-step explanation:

In quad. DPBQ, by angle sum property we have

∠PDQ + ∠DPB + ∠B + ∠BQD = 360°

60° + 90° + ∠B + 90° = 360°

∠B = 360° – 240°

Therefore, ∠B = 120°

But ∠B = ∠D = 120°    opposite angles of parallelogram 

As, AB || CD      opposite sides of a parallelogram

∠B + ∠C = 180°     sum of adjacent interior angles is 180°

120° + ∠C = 180°

∠C = 180° – 120° = 60°

Hence ∠A = ∠C = 60°    Opposite angles of parallelogram are equal

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