Find the value of x in the following - Maths - Lines and Angles

Question

Find the value of x in the following

Atul Shaw · Accepted Answer

Dear student,
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As AC=ABSo, ∠ACB=∠ABC=x∠ACB+∠ACD=180°   (Linear Angle)⇒x+∠ACD=180°⇒∠ACD=180°-xAs AC=CDSo, ∠CAD=∠CDA=yin △ACD,∠ACD+∠CDA+∠DAC=180° (Sum of angles of a △)⇒180°-x+y+y=180°⇒2y=x⇒y=x2So, ∠CAD=x2in △ACB,∠ACB+∠ABC+∠CAB=180°⇒x+x+∠CAB=180°⇒∠CAB=180°-2xNow,∠DAC+∠CAB+96°=180° (Linear Angle)0
5x+180°-2x+96°=180°96°=1 5xx=64°Regards