(a) A number is selected at random from each of the sets {2, 3, 4}

Explanation

Sample space = 9

Sum greater than 3 but less than 7 = {5, 4, 6, 5} = 4

P(sum greater than 3 but less than 7) = \(\frac{4}{9}\).

(b) Given that y + m = 90°

< ABE = x° (vertically opp. angles)

< BAD = (x + m)° (exterior angles)

< DCB = (x + y)° (exterior angles)

(x + m)° + (x + y)° = 180° (opp. angles of a cyclic quadrilateral)

(2x + y + m)° = 180°

(2x + 90) = 180

2x = 180 - 90 = 90°

x = 45°