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

Respuesta :

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!

abidemiokin

The measure of the angle between the diagonals, which lies opposite to a shorter side is 54 degrees

Complementary angles

The angle formed by the diagonal and the angle between the diagonals, which lies opposite to a shorter side is complementary i.e their sum is equal to 90 degrees.

Let the required angle be x, hence;

x + 36 = 90
x = 90 - 36

x = 54 degrees

Hence the measure of the angle between the diagonals, which lies opposite to a shorter side is 54 degrees

Learn more on complementary angles here: https://brainly.com/question/16281260

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