Key facts

  • Angles around a point add to 360°, angles on a straight line add to 180°, and vertically opposite angles are equal.
  • A linear pair is formed by two adjacent angles whose non-common arms make a straight line; its angle sum is always 180°.
  • Triangle angles add to 180°; a quadrilateral adds to 360°, and an n-sided rectilinear figure has interior-angle sum (n - 2) × 180°.

Key Points at a Glance

  1. 1

    Angles around a point add to 360°, angles on a straight line add to 180°, and vertically opposite angles are equal.

  2. 2

    A linear pair is formed by two adjacent angles whose non-common arms make a straight line; its angle sum is always 180°.

  3. 3

    When a transversal cuts parallel lines, corresponding and alternate interior angles are equal, while co-interior angles are supplementary.

  4. 4

    Triangle angles add to 180°; a quadrilateral adds to 360°, and an n-sided rectilinear figure has interior-angle sum (n - 2) × 180°.

  5. 5

    Congruent triangles are equal in shape and size; SSS, SAS, ASA/AAS and RHS are valid congruence tests, but AAA gives only similarity.

  6. 6

    In a right triangle, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, and tan θ = opposite/adjacent.

  7. 7

    Heights and distances questions become easy after drawing a right triangle, marking the angle of elevation or depression, and choosing the ratio that contains the required side.

  8. 8

    Common CET errors in this topic come from using the wrong angle pair, treating similarity as congruence, or mixing height and horizontal distance.

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Lines and angles at a point

An angle is formed when two rays start from the same point. The common starting point is the vertex, and the two rays are the arms of the angle. For CET, the first task is not proof but correct identification: is the question asking about a straight line, a full turn, opposite angles, or adjacent angles?

A straight angle is 180°. In words, it is the angle made by a ray when it turns exactly half a rotation and forms a straight line. If point O lies on a straight line AB, then ∠AOB = 180°. Any angles placed along that straight line and sharing point O must together add to 180°.

A complete angle is 360°. It represents one full rotation around a point. If several angles are drawn around point O without gaps, their total is 360°. For example, if four angles around a point are 70°, 95°, 110° and x°, then x = 360 - (70 + 95 + 110) = 85°.

Adjacent angles have a common vertex, a common arm, and interiors that do not overlap. If ∠AOB and ∠BOC share arm OB and lie on different sides of OB, they are adjacent. A linear pair is a special case of adjacent angles: the two non-common arms form a straight line. Therefore, a linear pair is supplementary. If one angle of a linear pair is 124°, the other is 56°.

Vertically opposite angles are formed when two lines intersect. The opposite angles, not the neighbouring ones, are equal. If two lines cross at O and one angle is 65°, the angle directly opposite it is also 65°. The two adjacent angles beside it are 180 - 65 = 115° each. In MCQs, a small diagram may show X-shaped lines; first mark the equal opposite angles, then use the straight-line sum for the remaining pair.

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