Answer:m∠J = 45° , m∠I = 45° and m∠M = 90°And the ΔJIM is an isosceles right angled triangle.Step-by-step explanation:(a). In ΔJIM,∠J = 2x + 15,∠I = 5x - 30, and ∠M = 6xNow, using angle sum property of a triangle that sum of all the angles in a triangle is 180°⇒ ∠J + ∠I + ∠M = 180°⇒ 2x + 15 + 5x - 30 + 6x = 180°⇒ 13x -15 = 180°⇒ 13x = 195⇒ x = 15Therefore, m∠J = 45° , ∠I = 45° and m ∠M = 90°(b). Now, ΔJIM is a right angled triangle right angled at M.Also, ∠J = ∠I = 45°So, JM = IM ( because in a triangle sides opposite to equal angles are equal)So, ΔJIM is an isosceles triangle because its two sides are equal.Hence, ΔJIM is a right angled isosceles triangle right angled at M.