ABCD is a rhombus- IF - BAC - 38-find1 -ACB2 -DAC3 -ADC

ABCD is Rhombus (Given) AB = BC ∠ BAC=∠ ACB(∠ S opp.To equal sides) But ∠ BAC=38^∘(Given) ∠ ACB = 38^∘ In ABC, ABC+∠ BAC+ ∠ ACB= 180^∘ angle ABC + 38^∘ + ...

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Standard IX

Mathematics

Diagonals of a Rhombus are Perpendicular to Each Other

ABCD is a rho...

Question

ABCD is a rhombus. IF $∠ B A C = 38^{\circ},$ find
(1) $∠$ ACB
(2) $∠$ DAC
(3) $∠$ ADC

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Solution

ABCD is Rhombus (Given)
AB = BC
$∠ B A C = ∠ A C B (∠ S o p p . T o e q u a l s i d e s) B u t ∠ B A C = 38^{\circ} (G i v e n) ∠ A C B = 38^{\circ} I n △ A B C, △ A B C + ∠ B A C + ∠ A C B = 180^{\circ} a n g l e A B C + 38^{\circ} + 38^{\circ} = 180^{\circ} ∠ A B C = 180^{\circ} - 76^{\circ} = 104^{\circ} ∠ A D C = ∠ A B C (O p p . ∠ s o f r h o m b u s) ∠ A D C = 104^{\circ} ∠ D A C = ∠ D C A (A D = C D) ∠ D A C = 1 / 2 [180^{\circ} - 104^{\circ}] ∠ D A C = 1 / 2 \times 76^{\circ} = 38^{\circ}$

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$ABCD is a rhombus. if ∠ B A C = 38^{\circ}, f i n d : (i) ∠ A C B (i i) ∠ D A C (i i i) ∠ A D C .$

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ABCD is a rhombus. IF ∠BAC=38∘,find (1) ∠ACB (2) ∠DAC (3) ∠ADC

ABCD is a rhombus. IF $∠ B A C = 38^{\circ},$ find
(1) $∠$ ACB
(2) $∠$ DAC
(3) $∠$ ADC