Question

In the given fig, ABCD is a square whose diagonal BD is extended
through D to E. AD=DE and AE is joined. Find the measure of DAE.​

Answer 1

Answer:

easy ans is 45/2

Step-by-step explanation:

Answer 2

Answer:

The measure of angle DAE is 45°.

Step-by-step explanation:

From the above question,

They have given :

In a square, the diagonal BD bisects each of the angles at the vertices A and C. So, angle ABD = angle CBD = 45°.

The given figure has a square ABCD with diagonal BD, which is extended through D to point E. AD is equal to DE and AE is joined. To find the measure of DAE, we can use the property of a right triangle. Since the sides AB and DE form a right triangle, we can use the Pythagorean Theorem to calculate the measure of DAE.

Since,

      AD = DE, triangle ADE is isosceles, so angle DAE = angle DEA = 45°.

Since angle ABD + angle DAE = 90°,

The Pythagorean Theorem states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. In this case, we know that AD = DE = side a, and AE = hypotenuse = side c.

We can use the Pythagorean Theorem to calculate the measure of DAE:

$a^2 + b^2 = c^2$

$(AD)^2 + (AE)^2 = (DE)^2$

$(DE)^2 + (AE)^2 = (DE)^2$

$AE^2 = DE^2$

$AE = \sqrt{DE^2}$

$AE = DE$

Therefore, the measure of DAE is equal to the measure of ADE, which is equal to DE.

we have:

angle ABD + angle DAE = 45° + 45° = 90°

Therefore, the measure of angle DAE is 45°.

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