in a quadrilaterel ABCD , AB parrelel CD,AD=CD and angle BAC=35 degree find angle ADC - Maths - Quadrilaterals

Question

in a quadrilaterel ABCD , AB parrelel CD,AD=CD and angle BAC=35
degree find angle ADC

Manbar Singh · Accepted Answer

Since, AB∥DC and AC is a transversal, then   ∠ACD = ∠BAC  Alternate interior angles⇒∠ACD = 35°In ∆ADC,      DA = DC  Given⇒∠ACD = ∠DAC   Angles opposite to equal sides are equal⇒∠DAC = 35°In ∆ADC,∠ADC + ∠ACD + ∠DAC = 180°  Angle sum property⇒∠ADC + 35° + 35° = 180°⇒∠ADC  = 180°-70° = 110°