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In a rectangle, one diagonal is inclined to one of its sides at 25°. Measure the acute angle between the two diagonals.

 In a rectangle, one diagonal is inclined to one of its sides at 25°. Measure the acute angle between the two diagonals.

 

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5962 Points
one year ago
Dear Student

Let ABCD be a rectangle where AC and BD are the two diagonals which are intersecting at point O.

Now, assume ∠BDC = 25° (given)

Now, ∠BDA = 90° – 25° = 65°

Also, ∠DAC = ∠BDA, (as diagonals of a rectangle divide the rectangle into two congruent right triangles)

So, ∠BOA = the acute angle between the two diagonals = 180° – 65° – 65° = 50°

Thanks

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