Question

ABCD is a kite
find the value of x

Answer 1

Since ABCD is a kite,

AD = CD (adjacent sides are equal in a kite)

and the diagonals intersect at right angles

Mark the intersecting point of diagonals as O.


Now, in ∆ADC,

AD = CD

Hence ∆ is isosceles triangle.
So, angle DCA = angle DAC = 50°

Now, in ∆AOB,

angle AOB = 90° (diagonal intersect at right angles)

and angle OBA = 36°

So, by angle sum property,

angle OAB + 36 + 90 = 180°

=> angle OAB = 180 - 90 - 36

=> angle OAB = 54°

now, x = angle OAB + angle DAC

=> x = 54 + 50

=> x = 104°

Hope it helps dear friend ☺️

Answer 2

Given:

ABCD is a kite

Angle DCA=50°

Angle DBA=36°

To find:

The value of x

Solution:

The required measure is 104°.

We know that the pair of the kite's adjacent sides are equal.

So, AD=DC and AB=BC.

We get that angle DAC=angle DCA.

Similarly, angle BAC=angle BCA. (Angles corresponding to equal sides are also equal)

Using the given values,

Angle DAC=Angle DCA=50°

Now, AC and BD meet each other at 90°.

Let the intersection of the diagonals be point O.

In ΔBOA, angle BOA=90°.

Angle BAC+angle BOA+angle DBA=180°

Using the values,

Angle BAC+90°+36°=180°

Angle BAC=180°-126°

Angle BAC=54°

We know that x=angle DAC+angle BAC.

x=50°+54°

x=104°

Therefore, the required measure is 104°.