Which of the following are the angles of a scalene triangle?

Correct — A. Option (a) reads 60°, 30° and 90°.
Sum check: 60 + 30 + 90 = 180°, so it is a genuine triangle.

Now compare the angles with each other: all three are different.
Equal angles sit opposite equal sides, so three unequal angles force three unequal sides — and a triangle with no two sides equal is scalene.

The right angle does not disqualify option (a). A triangle can be right-angled and scalene at the same time, and the 30-60-90 triangle is the standard example.

Why the others are wrong

• (b)
  110°, 35° and 35° has two equal angles, so the two sides opposite them are equal — that is isosceles, not scalene. It adds to 180°, so it is a real triangle; it is just the wrong type.
• (c)
  60°, 60° and 60° is the equilateral triangle, the exact opposite of scalene: all three angles equal means all three sides equal.
• (d)
  90°, 45° and 45° is a right-angled isosceles triangle. The two 45° angles make the two legs equal, so it fails the no-two-sides-equal test.

A triangle carries two independent labels: one from its sides (scalene, isosceles, equilateral) and one from its angles (acute, right, obtuse).

The bridge between the two is that equal angles sit opposite equal sides. So a triangle whose three angles are all different must have three different sides, which is exactly what scalene means. You never have to look at the sides here — the angle list settles it.

Key facts

• The angles of any triangle sum to 180°.
• Equal angles lie opposite equal sides, so all-different angles means all-different sides — the definition of scalene.
• Equilateral triangles are exactly the 60°-60°-60° ones.
• A right-angled triangle may be scalene (30-60-90) or isosceles (45-45-90).

Common traps

• Reading scalene as 'no right angle' and rejecting the 90° option.
• Stopping at the angle-sum check, which all four options pass.
• Confusing scalene with isosceles when two of the three numbers merely look close.

No directly related past PYQ was found.