Question

ABCD is a rhombus with angle ABC =50° Determine angle ACD.​

Answer 1

Answer:

⇒ ABCD is a parallelogram

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

⇒ ABCD is a parallelogram∴∠ADC = ∠ABC = 50°[opp angles of a parallelogram are equal] ∵ Adjacent sides of a rhombus are equal

⇒ ABCD is a parallelogram∴∠ADC = ∠ABC = 50°[opp angles of a parallelogram are equal] ∵ Adjacent sides of a rhombus are equal ∴ AD = AC

⇒ 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

⇒ 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)

⇒ 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

⇒ 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°

⇒ 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°

⇒ 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° .

Answer 2

Answer:

from figure, we have

∠ABC+∠BCD=180

∴∠BCD=180−50

and ∠BCD=130

∠ACD=21∠BCD

∠ACD=21×130

∠ACD=65degree