a) Two angles are said to be complementary if their sum is equal to 90°
Given : 2x and 4x are complementary angles
⇒ 2x + 4x = 90°
⇒ 6x = 90°
⇒ x = 15°
Answer: The two angles are : 30° and 60°
b) Two angles are said to be supplementary if their sum is equal to 180°
Given : x and 5x are supplementary angles
⇒ x + 5x = 180°
⇒ 6x = 180°
⇒ x = 30°
Answer: The two angles are : 30° and 150°
c) Two angles are said to be complementary if their sum is equal to 90°
Given : x and x + 50° are complementary angles
⇒ x + x + 50° = 90°
⇒ 2x = 40°
⇒ x = 20°
Answer: The two angles are : 20° and 70°
d) If two angles form a linear pair, then the sum of the angles should be equal to 180°
Given : 2x + 10° and 3x + 10° form a linear pair
⇒ 2x + 10° + 3x + 10° = 180°
⇒ 5x = 160°
⇒ x = 32°
⇒ 2x + 10° = 2(32) + 10° = 74°
⇒ 3x + 10° = 3(32) + 10° = 106°
Answer: The two angles are 74° and 106°
