IMO Practice Test — Angle Relationships
6 Questions • 25 min • Olympiad level
25:00
Question 1 of 6
hard
Two complementary angles differ by 20°. Find larger angle.
35°
45°
55°
65°
Explanation: x+(x-20)=90, 2x=110, x=55°
Question 2 of 6
hard
Supplement of an angle is 4 times its complement. Find the angle.
30°
45°
60°
75°
Explanation: 180-x=4(90-x), 180-x=360-4x, 3x=180, x=60°
Question 3 of 6
hard
In intersecting lines, one angle is 3x, adjacent is 2x. Find x.
18°
20°
24°
36°
Explanation: 3x+2x=180, 5x=180, x=36°
Question 4 of 6
hard
Triangle angles: x, 2x, 3x. Find largest angle.
60°
90°
100°
120°
Explanation: x+2x+3x=180, 6x=180, x=30, largest=90°
Question 5 of 6
hard
Isosceles triangle has vertex angle 40°. Find base angles.
40°,40°
70°,70°
50°,50°
80°,80°
Explanation: Base angles equal, 180-40=140, ÷2=70°
Question 6 of 6
hard
Angle A and B are complementary. Angle B and C are supplementary. If A=35°, find C.
55°
125°
145°
155°
Explanation: A=35, B=55 (complement), C=180-55=125°