ABCD is a rhombus with ∠ABC = 50°. Determine ∠ACD .
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
∴ In △ACD we have
∠DAC + ∠ACD + ∠ADC = 180° ⇒ x + x + 50°= 180°
⇒ 2x = 30° ⇒ x = 65°
∴ ∠ACD = 65° .
Angle ABC=angle ADC
In Triangle ADC, by asp
Angle ADC =65