Question

in figure, ABCD is a rhombus. Find the value of x​

Answer 1

Answer:

x is 54°.

explanation- the diagonals bisect each other at 90°

so angle AOD=90°

in triangles ACD and ACB

AB=AD

BC=CD

AC=AC

So triangles ACD is congruent to ACB

By CPCT, Angle BAC=Angle DAC

Angle DAC=36°

DAO+AOD+x=180°

36°+90°+x=180°

126°+x=180°

x=180-126

x=54°

Answer 2

Given,

A figure of rhombus ABCD.

Two diagonals bisect at O.

∠OAB= 36°.

To Find,

The value of x which is equal to ∠ODA.

Solution,

We know from the property of Rhombus that the diagonals of any such Rhombus with any length bisect each other at the angle of 90°.

Hence, here two diagonals AC and BD bisect each other at point O at an angle of 90°.

∴∠AOD=90°.

Now if we seeΔ ACD and ΔACB, in those triangles,

AB=AD and BC=CD [As the sides of Rhombus are equal]

AC common line

So  Δ ACD is congruent to the Δ ACB.

So, we can say, Angle BAC=Angle DAC

As∠BAC=36°, therefore ∠ DAC=36°.

Now for ΔAOD.we can say.

∠DAO+∠AOD+x°=180°

⇒36°+90°+x°=180°

⇒126°+x°=180°

⇒x°=180°-126°

⇒x°=54°

Hence, the value of x is 54°.