Similar triangles means all angles of one triangle are same as the other triangle . Triangle BAC and DAE are equal by construction as they lie within the same rays. Triangle BCA and DEA are right angles. Sum of all angles of triangle is 180 degree. Since two of the angles are same say X and 90, the third has to be the same such that ABC and ADE are both 180- X -90 Ie 90-X.
