The ratio between a base angle and a vertical angle of an isosceles triangle base angles being equal...........

Quantitative Aptitude (CPO) Geometry

The ratio between a base angle and a vertical angle of an isosceles triangle (base angles being equal) is 2 :5. The vertical angle is:

This questions was previously asked in

SSC CPO 15th-March-2019-Shift-2

140^o

40^o

100^o

80^o

- In an isosceles triangle, the two base angles are equal.

- Let each base angle be 2x and the vertical angle be 5x.

- The sum of angles in a triangle is always \(180^\circ\).

- Therefore, \(2x + 2x + 5x = 180\).

- Simplifying, \(9x = 180\).

- Solving for x, we get \(x = 20\).

- Thus, the vertical angle, which is 5x, is \(5 \times 20 = 100\).

- Option 1: 140°, not possible as 5 times 20 is not 140.

- Option 2: 40°, too small to be the vertical angle.

- Option 3: 100°, matches the calculation.

- Option 4: 80°, doesn't match the vertical angle calculation.

- Correct Answer: Option 3 - 100^o

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