#### Question

ABCD is a cyclic quadrilateral in which BC is parallel to AD, angle ADC = 110° and angle BAC = 50°. Find angle DAC and angle DCA.

#### Solution

ABCD is a cyclic quadrilateral in which AD||BC

`∠`ADC = 110° , `∠`BAC = 50°

`∠`B + `∠`D = 180°

(Sum of opposite angles of a quadrilateral)

⇒ `∠`B + 110° = 180°

⇒ `∠`B = 70°

Now in ΔABC,

`∠`BAC + `∠`ABC + `∠`ACB = 180°

⇒ 50° + 70° + `∠`ACB = 180°

⇒ `∠`ACB = 180° - 120° = 60°

∵ AD ll BC

∴ `∠`DAC= `∠`ACB = 60° (alternate angles)

Now in ΔADC,

`∠`DAC + `∠`ADC +`∠`DCA = 180°

⇒ 60° + 110° ` +∠`DCA = 180°

⇒ `∠`DCA = 180° - 170° = 10°

Is there an error in this question or solution?

Solution Abcd is a Cyclic Quadrilateral in Which Bc is Parallel to Ad, Angle Adc = 110° and Angle Bac = 50°. Find Angle Dac and Angle Dca. Concept: Cyclic Properties.