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Junior Cycle · Junior Cycle Maths

Junior Cycle Maths: Angles & geometry theorems

How often Angles & geometry theorems comes up on the Maths papers, every year it was asked, and questions to try.

HL Asked on 5 of the last 5 Higher Level papers, most recently in 2026. banker

OL Asked on 4 of the last 5 Ordinary Level papers, most recently in 2026. most years

Angles & geometry theorems, Higher Level(8 marks)

Quick ones on Angles & geometry theorems.

(a)The angles of a triangle are x, 2x and 3x. What is the largest angle?
  1. 60°
  2. 90°
  3. 30°
(b)An exterior angle of a triangle is 115°. One interior opposite angle is 40°. What is the other one?
  1. 155°
  2. 65°
  3. 75°
(c)The angle at the centre of a circle standing on arc AB is 110°. An angle at the circle on the same arc is…
  1. 55°
  2. 220°
  3. 110°
Show the answers

(a) 90°

(b) 75°

(c) 55°

Your turn: Higher Level questions on Angles & geometry theorems.

Higher Level

Asked on 5 of the last 5 Higher Level papers, most recently in 2026. banker

Every paper, year by year

YearWhere it came up
2026Q12
2025Q6
2024Q9
2023Q7
2022Q8, Q12

Links open the State Examinations Commission’s paper for that year.

Ordinary Level

Asked on 4 of the last 5 Ordinary Level papers, most recently in 2026. most years

Every paper, year by year

YearWhere it came up
2026Q5
2025Not asked
2024Q5
2023Q13
2022Q7

Links open the State Examinations Commission’s paper for that year.

More Angles & geometry theorems questions

Angles & geometry theorems, 3 marks

An isosceles triangle has a vertex angle of 40°. What size is each base angle?

  1. 40°
  2. 140°
  3. 70°
Show the answer

70°

The base angles of an isosceles triangle are equal. The angles add to 180°, so 180 − 40 = 140 is shared equally: 140 ÷ 2 = 70°.

Angles & geometry theorems, 2 marks

Two parallel lines are cut by a transversal. One angle is 65°. What is its alternate angle?

  1. 25°
  2. 65°
  3. 115°
Show the answer

65°

Alternate angles (the Z shape) between parallel lines are equal, so the alternate angle is also 65°.

Angles & geometry theorems, 3 marks

A triangle has interior angles of 40° and 75°. What is the exterior angle at the third vertex?

  1. 115°
  2. 65°
  3. 105°
Show the answer

115°

An exterior angle equals the sum of the two interior opposite angles: 40 + 75 = 115°. The interior angle at that vertex is 65°.

Other Maths topics

All of Junior Cycle Maths