25 120 & Find the angles in each of the following: 65 (a) The angles are complementary and the smaller is 40° less than the larger. (b) The angles are complementary and the larger is four times the smaller. (c) The angles are supplementary and the smaller is one-half of the larger. (d) The angles are supplementary and the larger is 58° more than the smaller. (e) The angles are supplementary and the larger is 20° less than three times the smaller. (1) The angles are adjacent and form an angle of 140°. The smaller is 28° less than the larger.
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a) x + x - 40 = 2x - 40
2x - 40 = 90
2x = 130
x = 65°
another angle= 65-40 = 25°
b) x + 4x = 90
5x = 90
x= 18°
another angle= 4×18= 72°
c) x + x/2 = 180°
3x/2 = 180
x = (180×2)/3 = 120°
another angle = 120/2 = 60°
d) x+x+58 = 180
2x+58 = 180
2x = 122
x = 61°
another angle = 61+58 = 119°
e) x+3x-20 = 180
4x-20 = 180
4x = 200
x = 50°
another angle= 50×3 - 20 = 130°
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