Question

quadrilateral ABCD is a rhombus if angle DAC =35 then find the ANGLE ABC​

Answer 1

Answer:

To find : ∠ADC

Proof : AD || BC

∠DAC = ∠BCA (Alternate ∠s)

∠DCA = 35° (Given)

But ∠DAC = ∠ACD ( AD = CD) & ∠DAC + ∠ACD + ∠ADC = 180°

35° + 35° + ∠ADC = 180°

∠ADC = 180° – 70° = 110°

Hence ∠ADC = 110°

Answer 2

Given , Quadrilateral ABCD is rhombus

∠DAS = 35°

To find:- m ∠ABC

Solution :-

In Quadrilateral ABCD , ∠DAC= 35°

side AB ll side BC and transversal AC

m∠DAC=m∠ACB - alternate angles

but , m∠DAC = 35°

therefore , m∠ACB = 35°

But , ∠DAC= ∠ACD ( AD=CD)

∠DAC + ∠ACD +∠ADC=180°

35°+35° + ∠ADC=180°

70°+ ∠ADC = 180°

∠ADC=180°-70°

∠ADC= 110°

OPPOSITE ANGLES OF RHOMBUS ARE CONGRUENT

but , m∠ADC=110°

m∠ABC=110°

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