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Class 9th
Chapter Quadrilaterals
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Answer:
50
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- We are given that, a diagonal of a rectangle is inclined to one side of the rectangle at 25°.
- We need to find the acute angle between the diagonals is = ?
- So, first assume the acute angle between diagonals be m.
- As we know that, the diagonals of rectangle are equal in length. Hence, PR = QS.
- Divide both the sides by 2 and we get :
⇢½ PR = ½ QS
- Here, O is the midpoint of PR and QS. So we get :
⇢OS = OR
- As we know that, angle opposite to the equal sides are equal. Hence we get :
⇢m∠OSR = m∠n = 25°
- Exterior angles of a ∆ is equal to the sum of the two opposite interior angles :
⇢∠QOR = ∠OSR + ∠ORS
⇢∠m = = 25° + ∠n
⇢∠m = 25° + 25°
⇢∠m = 50°
- Therefore, the acute angle between diagonals is 50°.
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