Question

abcd is rhombus with angle=50,determine angle abcd

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° .