ABCD is a rhombus- If - BCA -35- then - ADC -A- 90-B- 110-C- 60-D- 115-

The correct option is B 110^∘ ⇒∠ DAC = ∠ BCA [Alternate Angles] ⇒ Given ∠ BCA = 35^∘ ⇒∠ DAC = nbsp;35^∘ ⇒ nbsp; ∠ DAC = ∠ ACD [AD = CD] ⇒ nbsp; ∠ DAC ...

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Byju's Answer

Standard VIII

Mathematics

Quadrilaterals and Their Properties

ABCD is a rho...

Question

ABCD is a rhombus. If $∠ B C A = 35^{\circ}$ then

$∠ A D C =$ ___.

$90^{\circ}$

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$110^{\circ}$

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$60^{\circ}$

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$115^{\circ}$

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Solution

The correct option is B
$110^{\circ}$

$\Rightarrow ∠ D A C = ∠ B C A [A l t e r n a t e A n g l e s]$

$\Rightarrow G i v e n ∠ B C A = 35^{\circ}$

$\Rightarrow ∠ D A C = 35^{\circ}$

$\Rightarrow ∠ D A C = ∠ A C D [A D = C D]$

$\Rightarrow ∠ D A C + ∠ A C D + ∠ A D C = 180^{\circ}$

$\Rightarrow 35^{\circ} + 35^{\circ} + ∠ A D C = 180^{\circ}$

$\Rightarrow ∠ A D C = 180^{\circ} - 70^{\circ} = 110^{\circ}$

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ABCD is a rhombus. If ∠BCA=35∘ then ∠ADC= ___.

The correct option is B 110∘ ⇒∠DAC=∠BCA [Alternate Angles] ⇒Given ∠BCA=35∘ ⇒∠DAC=35∘ ⇒∠DAC=∠ACD [AD=CD] ⇒∠DAC+∠ACD+∠ADC=180∘ ⇒35∘+35∘+∠ADC=180∘ ⇒∠ADC=180∘−70∘=110∘

ABCD is a rhombus. If $∠ B C A = 35^{\circ}$ then

$∠ A D C =$ ___.