Q3.Given that ABC is an equilateral triangle and BDC is an isosceles right triangle,right angled at D, with a common base BC.Find the measure of ABD. Share with your friends Share 3 Tanveer Sofi answered this The triangle ABC is equilateral triangle, then all its angles measure 60∘. Then ∠ ABD= 60∘.Now, triangle BDC is an isosceles triangle and right angled at D, ∠ BDC=90∘ and two angles of a triangle cannot be equal to 90∘.The only possibility is ∠ CBD=∠ DCBAlso, the sum of angles of a triangle is 180∘, therefore∠ CBD+∠ DCB+∠ BDC= 180∘⇒∠ CBD+∠ CBD+ 90∘= 180∘ As, ∠ CBD=∠ DCB⇒2 ∠ CBD= 90∘⇒∠ CBD= 45∘.Now, from the above figure∠ ABD= ∠ ABC+∠CBD= 90∘+ 45∘=135∘. 4 View Full Answer