Geometry · Topic 1 of 7

📐 Lines & Angles

2 exam question types, fully solved

Almost every geometry question starts with a few angle rules. Learn these handful of facts cold and you can read off most missing angles in seconds instead of guessing from the figure.

The angle facts that crack most questions

• Straight line: angles sitting on one side of a straight line add to — a linear pair. Two angles that add to are supplementary; two that add to are complementary.

• Around a point: all the angles meeting at a single point add to (one full turn).

• Vertically opposite: when two lines cross, the angles facing each other are equal.

• Triangle: the three interior angles of any triangle add to , so two known angles fix the third.

• Parallel lines cut by a transversal (): corresponding angles are equal (the F-shape), alternate angles are equal (the Z-shape), and co-interior / same-side angles are supplementary, i.e. they add to (the C-shape).

The exam habit to build: write the rule as an equation first ( or ), drop the known values in, and solve in one line — never measure off the drawing.

📐Angle ExplorerTilt the transversal — watch all 8 angles change

Corresponding (F-shape) — EQUAL∠2 = ∠6 → 60° = 60°

Every angle is either60° or 120°

Linear pair check60° + 120° = 180°

Two parallel lines are cut by a transversal and one co-interior angle is . Since co-interior angles add to , its partner is = .

Q1Two parallel lines are cut by a transversal. One co-interior angle is 110°. The other co-interior angle is:

Q2AB ∥ CD and a transversal makes a 75° angle. Its alternate interior angle is:

Q3Two angles of a triangle are 55° and 65°. The third angle is:

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Real exam questions — Lines & Angles

2 question types · 9 solved examples from real SSC papers

Most angle questions fall out of a few rules: angles on a line make 180 degrees, and parallel lines cut by a transversal create equal and supplementary pairs.

How to solve this type

Lock in the four core facts. (1) Angles on a straight line (a linear pair) add to

180^\circ

— these are supplementary. (2) Angles round a point add to

360^\circ

. (3) When two lines cross, vertically opposite angles are equal. (4) Two angles are complementary if they add to

90^\circ

. For any triangle the three interior angles add to

180^\circ

, so once two are known the third is forced. Build the habit: write the angle-sum equation first, then put the known values in and solve in one line.

Three angles of a triangle are $(x-15)^\circ$ , $(x+45)^\circ$ and $(x+60)^\circ$ . What type of triangle is it?

AObtuse-angledBRight-angledCIsoscelesDEquilateral

In $\triangle ABC$ the bisectors of $\angle B$ and $\angle C$ meet at a point $O$ inside the triangle. If $\angle BOC = 122^\circ$ , find $\angle A$ .

72^\circ

62^\circ

68^\circ

64^\circ

If $\triangle ABC \cong \triangle PQR$ and $\angle B = 35^\circ$ , then what is $\angle P + \angle C$ ?

116^\circ

120^\circ

130^\circ

145^\circ

In $\triangle XYZ$ , $A$ is a point on $YZ$ with $XA = YA$ . If $\angle XYA = 50^\circ$ and $\angle AXZ = 19^\circ$ , find $\angle XZA$ .

61^\circ

53^\circ

49^\circ

41^\circ