Question

ABCD is a rhombus .if angle DAC =50°,FIND (A) angle ACD (B) ANGLE CAB (C) ANGLE ABC.​

Answer 1

Answer:

80Degree

Sep-by-step explanation:

ABCD is a rhombus.

angle DAC=50,

We have to find: a)angle ACD b) angle CAB (c)angle ABC.

∠DAC = 50°

ABCD is a rhombus.  => AB = BC = CD = AD

rhombus is a parallogram also

hence AB || CD and BC || AD

in ΔACD  AD = CD

Hence ∠ACD = ∠DAC

=> ∠ACD = 50°

AB || DC

∠CAB  =  ∠ACD    ( interior alternate angles)

=> ∠CAB  =  50°

in  ΔABC  

AB = BC  Hence ∠ACB = ∠CAB =  50°

∠ACB + ∠CAB + ∠ABC = 180°

=> 50° + 50° + ∠ABC = 180°

=>  ∠ABC =  80°

Answer 2

Answer:

ABCD is a rhombus.

AB=BC=CD=AD

ABCD is a rhombus

∠ABC=∠ADC

∠BAD=∠BCD

∠DAC=∠BCA=50°

$50 + x + y + 50 + x + y \\ \\ = 2x + 2y = 260 \degree \\ \\ x + y = 130 \degree$

Diagonal bisect the angles

x=50° y=130-50=80°