Question

ABCD is a rhombus if ∠BAC =38 degree find [1] ∠ACB [2] ∠DAC [3] ∠ ADC

Answer 1

Answer

Step-by-step explanation:

• Given :

ABCD is a rhombus if ∠BAC =38°

• To Prove :

[1] ∠ACB

[2] ∠DAC

[3] ∠ ADC

• Proof :

(1) <ACB

As we know that in a rhombus opposite angles are equal

=> <DAB = <DCB

Also the diagonal of a rhombus bisects the angles .

So , <DAC = <CAB = 38°.

=> <ACB = <DAC = 38°. (alternate angles)

(2) <DAC

As proved above that <DAC = <CAB = 38°.

(3) <ADC

As said above that in a rhombus opposite angles are equal .

So <CBA = <ADC

We know that <DAC + <CAB = <DAB

= 38° + 38° = 76°.

As AB || CD and AD and BC are transversal,

<DAB + <CBA = 180° ( co-interior angles)

= 76° + <CBA = 180°

= <CBA = 180° - 76°

=> <CBA = 104°.

∴ Hence proved