ABCD is a rhombus- If -DAC - 25- then the measure of -ABC is-

Given: ∠ DAC=25^∘ To find: ∠ ABC ∠ BAC=∠ DAC=25^∘ [ Diagonal AC bisects the ∠ DAB ] ∠ DAB= ∠ BAC+∠ DAC ∠ DAB=25^∘+25^∘=50^∘ nbsp; Now, ∠ DAB+∠ ABC=180^∘ ...

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Standard VIII

Mathematics

Quadrilaterals

ABCD is a rho...

Question

$ABCD$ is a rhombus. If $∠ DAC = 25^{\circ}$ , then the measure of $∠ ABC$ is.

155^{\circ}

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130^{\circ}

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65^{\circ}

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Solution

The correct option is B $130^{\circ}$
Given: $∠ D A C = 25^{\circ}$
To find: $∠ A B C$

$∠ B A C = ∠ D A C = 25^{\circ}$
[ Diagonal AC bisects the $∠ D A B$ ]

$∠ D A B = ∠ B A C + ∠ D A C$

$∠ D A B = 25^{\circ} + 25^{\circ} = 50^{\circ}$

Now, $∠ D A B + ∠ A B C = 180^{\circ}$
[Adjacent angles of a parallelogram]

$∠ A B C = 180^{\circ} - ∠ D A B$

$∠ A B C = 180^{\circ} - 50^{\circ} = 130^{\circ}$

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ABCD is a rhombus. If ∠DAC=25∘, then the measure of ∠ABC is.

The correct option is B 130∘Given: ∠DAC=25∘ To find: ∠ABC ∠BAC=∠DAC=25∘ [ Diagonal AC bisects the ∠DAB ] ∠DAB=∠BAC+∠DAC ∠DAB=25∘+25∘=50∘ Now, ∠DAB+∠ABC=180∘ [Adjacent angles of a parallelogram] ∠ABC=180∘−∠DAB ∠ABC=180∘−50∘=130∘

$ABCD$ is a rhombus. If $∠ DAC = 25^{\circ}$ , then the measure of $∠ ABC$ is.