Practice30Create account

Two straight lines cross at a point. Taken in order round the point, the four angles are in the ratio 5 : 4 : 5 : 4. Find the larger angle.

Class 7Lines and AnglesLines and Angles
  • A80°
  • B200°
  • C50°
  • D100°

Step-by-Step Solution

Angles round a point total 360°, and the parts total 5 + 4 + 5 + 4 = 18, so one part = 360 ÷ 18 = 20°. The angles are 100°, 80°, 100°, 80° — the equal pairs are the vertically opposite ones, and 100 + 80 = 180 confirms each linear pair. The larger is 100°. Trap: 80° is the smaller angle; 200° comes from ignoring that the ratio lists FOUR angles.
Answer: D) 100°

Key idea: Vertically opposite angles

When two straight lines cross, four angles form at the intersection. The two angles directly **across** the vertex (sharing only the vertex, not a side) are called **vertically opposite** — and they are always equal.

If one angle is 70°, then:
- Its vertical opposite is also 70°.
- The other two angles are each 110° (linear pair with 70°).

Why? Each pair forms a linear pair with a common neighbour, both summing to 180° — so the opposites end up equal.

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Lines and Angles practice questions

More Class 7 Lines and Angles practice

Find the complement of the supplement of 145°.A ladder leans against a vertical wall that meets the level ground at a right angle. The…A see-saw plank rests on a pivot. On one side the plank makes an angle of 24° with the…Three straight lines all pass through a single point O, so six angles are formed around…Two parallel lines are cut by a transversal. A pair of angles lies OUTSIDE the parallel…