IMO Practice Test — Lines and Angles
6 Questions • 15 min • Olympiad level
15:00
Question 1 of 6
hard
In triangle ABC, ∠A = 50° and ∠B = 70°. Find the exterior angle at C.
60°
120°
130°
140°
Explanation: Exterior at C = ∠A+∠B = 50°+70°=120°
Question 2 of 6
hard
Two complementary angles differ by 20°. Find the larger angle.
35°
45°
55°
65°
Explanation: x + (x-20)=90 → 2x=110 → x=55°
Question 3 of 6
hard
In the figure, l ∥ m and ∠1 = 65°. Find ∠8.
65°
115°
125°
180°
Explanation: ∠1 and ∠8 are alternate exterior angles? Actually ∠1 and ∠5 correspond, ∠5 and ∠8 form linear pair → 180-65=115°
Question 4 of 6
hard
The angles of a triangle are (x+10)°, (2x-20)°, and (3x-50)°. Find x.
30
35
40
45
Explanation: Sum = 6x-60=180 → 6x=240 → x=40
Question 5 of 6
hard
If two parallel lines are cut by a transversal and the difference of two consecutive interior angles is 40°, find the smaller angle.
50°
60°
70°
80°
Explanation: Let angles be x and x+40. x+(x+40)=180 → 2x=140 → x=70°
Question 6 of 6
hard
In the given figure, AB ∥ CD and EF is a transversal. If ∠AEF = 65°, find ∠EFD.
65°
115°
125°
180°
Explanation: ∠AEF and ∠EFD are consecutive interior angles → 180-65=115°