Math, asked by vanshita14, 1 year ago

the angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60° . find the angles of a parallelogram.

Answers

Answered by mudassirgoriya
43

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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Answered by THEHALFWAYSPY
1

Answer:

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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Step-by-step explanation:

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