This question was previously asked in

UPSSSC Chakbandi Lekhpal Official Paper 3 (Held on : 1 Oct 2019 Shift 1)

Option 3 : 1/2

**Given:**

Angle A, B and C are in parallel series.

AM perpendicular to BC.

**Concept used:**

Angle sum property of triangle,

A + B + C = 180°

**Calculation:**

If the angles are in parallel series,

⇒ B - A = C - B

⇒ 2B = A + C ----(1)

By angle sum property of triangle,

⇒ A + B + C = 180°

From equation (1)

⇒ B + 2B = 180°

⇒ 3B = 180°

⇒ B = 60°

AM perpendicular to BC

So, in ΔABM

⇒ ∠AMB = 90°

Now the remaining ∠BAM = 30°

ΔAMB is a right-angled,

⇒ Cos 60° = BM/AB

⇒ 1/2 = BM/AB

**∴ The value of BM/AB is 1/2.**