Question

ABCD is a rhombus with ABC=500

. Determine ACD.​

Answer 1

Answer:

Since ABCD is a rhombus

⇒ ABCD is a parallelogram

∴∠ADC = ∠ABC = 50°[opp angles of a parallelogram are equal]

∵ Adjacent sides of a rhombus are equal

∴ AD = AC

⇒ ∠DAC = ∠ACD [angles opposite to equal sides are equal

= x(say)

∴ In △ACD we have

∠DAC + ∠ACD + ∠ADC = 180° ⇒ x + x + 50°= 180°

⇒ 2x = 30° ⇒ x = 65°

∴ ∠ACD = 65° .

hope it's help you

Answer 2

Step-by-step explanation:

Since ABCD is a rhombus

⇒ ABCD is a parallelogram

∴∠ADC = ∠ABC = 50°[opp angles of a parallelogram are equal]

∵ Adjacent sides of a rhombus are equal

∴ AD = AC

⇒ ∠DAC = ∠ACD [angles opposite to equal sides are equal

= x(say)

∴ In △ACD we have

∠DAC + ∠ACD + ∠ADC = 180° ⇒ x + x + 50°= 180°

⇒ 2x = 30° ⇒ x = 65°

∴ ∠ACD = 65° .

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