Answer:

m∠X = 60°

BX = 8 cm

BM = 4√3 cm

Step-by-step explanation:

The sum of the interior angles of a triangle is 180°

Given:

• m∠B = 30°
• m∠M = 90°

⇒ m∠B + m∠M + m∠X = 180°

⇒ 30° + 90° + m∠X = 180°

⇒ 120° + m∠X = 180°

⇒  m∠X = 180° - 120°

⇒  m∠X = 60°

Using the sine rule to find the side lengths:

(where A, B and C are the angles, and a, b and c are the sides opposites the angles)

Given:

• m∠X = 60°
• m∠B = 30°
• m∠M = 90°
• MX = 4 cm

missing angle:

180° - 90° - 30°

180° - 120°

60°

missing sides:

(a)

(b)