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NeTakaya
2 years ago
15

In a rectangle, a diagonal forms a 36° angle with a side. Find the measure of the angle between the diagonals, which lies opposi

te to a shorter side.
Mathematics
1 answer:
bezimeni [28]2 years ago
8 0

Answer:

The answer is 72 degrees

Step-by-step explanation:

The picture that Helpmetnx showed does work. But they made a mistake and assumed that the diagonal is a angle bisector, and it's not.

1. rectangle ABCD, BD & AC are the diagonals. ∠ABD =36 degrees

2. ∠ABD= ∠BDC = 36 - alternate interior angles

3. ∠DBC = 90 - 36 = 54. ∠DBC =∠ADB = ∠BCA = 54

4. Now we know that the triangle formed between the two diagonals is a isosceles triangle because of base angle theorem.

5. 180 - 54*2 = 72 degrees

I hope this helps!

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To see , try starting at length 1, and gradually increase the length. 
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