The angles of triangle are such that one is average of other two, then the angles are:

Correct — B. Two tests decide this item, and it is the second one that separates the four printed sets.

Let C be the angle that is the average: C = (A + B)/2, so A + B = 2C.
Substitute into A + B + C = 180°: 2C + C = 180°
C = 60° — the averaged angle is always 60°.

Now apply the angle sum to the four sets in the figure:

1) π/6, π/3, π/2 = 30° + 60° + 90° = 180°
2) π/3, π/3, π/2 = 60° + 60° + 90° = 210°
3) π/6, π/3, π/4 = 30° + 60° + 45° = 135°
4) π/2, π/2, π/3 = 90° + 90° + 60° = 240°

Only set 1 is a triangle at all, and in it 60° = (30° + 90°)/2.
The figure numbers that set 1, which is option (b).

Why the others are wrong

• (a)
  3 — Option (a) points to set 3: π/6, π/3, π/4 = 30°, 60°, 45°. These add to 135°, not 180°, so they are not the angles of any triangle — the 60° in the middle is not enough on its own.
• (c)
  4 — Option (c) points to set 4: π/2, π/2, π/3 = 90°, 90°, 60°, which add to 240°. Two right angles cannot sit in one triangle, so the averaging condition never gets tested here.
• (d)
  2 — Option (d) points to set 2: 60°, 60°, 90°, which add to 210°. The closest trap in the paper — it holds the 60° the condition forces, but overshoots the 180° sum by 30°.

Two facts do all the work here. The angles of a triangle sum to 180°, and 'x is the average of y and z' means 2x = y + z.

Put them together and the averaged angle is pinned: if A + B = 2C, then 3C = 180°, so C = 60°.

The converse holds too. Any triangle with a 60° angle has the other two summing to 120°, so their average is 60° and the condition is met automatically.

So the condition is a disguised way of saying the triangle has a 60° angle — but three numbers still have to add to 180° before the word 'triangle' applies to them at all.

Key facts

• The three angles of a triangle sum to 180°.
• If one angle is the average of the other two, that angle is 60°, whatever the other two are.
• The four printed sets sum to 180°, 210°, 135° and 240° — only the first is a triangle.
• Set 1 is π/6, π/3, π/2 = 30°, 60°, 90°, and 60° = (30° + 90°)/2.

Common traps

• Testing the averaging condition and skipping the 180° sum — three of the four sets fail on the sum alone.
• Assuming every printed set adds to 180° because the question calls them 'the angles of triangle'.
• Reading 'average of the other two' as 'half of the largest', which sets up a different equation.

No directly related past PYQ was found.