Triangle ABC is an isosceles right angled at B and side BC is produced to D find angleACB

since its an isoceles triangle,so ab=bc n angle A = angle C. so applying the property of triangle, angleA+angleB+angleC =180. angleA+90+angleC=180.
2 of angleC+90=180
2of angleC=90
angle C=90/2
angle C=45
so ans is 45*

An isosceles right triangle always has a right angle at the vertex of the two equal sides. That is the 90 degree angle. The other two angles are 45 degrees, no matter what the length of the sides are, since they are equal.

Assume the equal sides are 1 unit, The hypotenuse will always be 2^(1/2) - the square root of 2. If the sides are 20, the hypotenuse will be sqrt(20^2+20^2) which is 20*2^(1/2)

Microsoft math has a triangle explorer which will help you understand this sort of thing.

Triangle ABC is isosceles=> 2 equal sides and 2 equal angles.
Triangle is also right angled=>one angle is 90 degree i.e B=90 degree
The remaining 2 angles of the triangle have to be equal and their sum is 90 degree.
A+B+C=180=>A+90+C=180=>A+C=90 and A=C Hence, A=C=90/2=45 degree
angle ACB= angle C = 45 degree.

OK. If you have an isosceles right triangle with
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Angle ACB is 45

Angle ACD is 135

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its 45 degree
do u need me to explain it?