UGC NET Questions (Paper – 1)

This option is correct because the sum of the interior angles of a triangle in Euclidean geometry is always 180 degrees. This can be shown using parallel lines and alternate interior angles. Every triangle can be thought of as half of a straight line angle sum. Therefore, the correct total is 180 degrees.

Option A:
90 degrees is the measure of a right angle, not the sum of all angles in a triangle. Only one angle in a right triangle is 90 degrees. Thus, this value is too small for the total.

Option B:
270 degrees exceeds the known sum of angles in a triangle and does not correspond to any standard triangle property. It is closer to the sum for different configurations, not a simple triangle. Hence, this option is not valid.

Option C:
360 degrees is the angle measure around a point, not inside a triangle. It equals the sum of interior angles of a quadrilateral, not a triangle. Therefore, it cannot be the correct answer.

Option D:
180 degrees is the established sum for any triangle in a plane. No matter the shape of the triangle, the three interior angles always add up to 180 degrees. This property is widely used in geometry problems, confirming this option as correct.

This option is correct because the sum of interior angles of a simple quadrilateral is known to be 360 degrees. A quadrilateral can be divided into two triangles, each having an angle sum of 180 degrees. Adding these gives 180 + 180 = 360. Therefore, the total interior angle sum is 360 degrees.

Option A:
A quadrilateral can be split into two triangles by drawing one diagonal. Each triangle has 180 degrees as the sum of its interior angles. Adding both triangle sums gives 360 degrees, so 360 is the correct total for the quadrilateral.

Option B:
180 degrees is the sum of interior angles of a single triangle, not a quadrilateral. Since a quadrilateral has more sides, its angle sum must be greater than that of a triangle. Thus, this option is not correct.

Option C:
270 degrees does not match any standard polygon angle-sum formula for quadrilaterals. It is less than the correct total of 360 degrees and therefore cannot be the right answer.

Option D:
540 degrees is the interior angle sum of a pentagon, not a quadrilateral. Using this value would assume five sides instead of four. Hence, this option is also incorrect.