Question

Find the angles in each of the following . Solve :-

a) The angles are supplementary and the larger is 20° less than 3 times the smaller .

b) The angles are complementary and the lager is 15° more than twice the smaller .

c) The angles are adjacent and form an angle of 120° . The larger is 20° less than 3 times the smaller.

d) The angles are vertical and complementary .
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Answer 1

Step-by-step explanation:

let the larger angle x

smaller angle y

x-20=3y

x-3y=20-----------1

x+y=180-----------2

subtract equation 1 from 2

x + y = 180

x -3y = 20

- + -

4y=160

y=40

put y in equation 2

x +y =180

x +40=180

x=180-40

x=140

Answer 2

a) Let the supplementary angles be x and y.
(X is the smaller angle and Y is the bigger angle)
Y = 3x - 20
Therefore, y + x = 180
Or 3x + x - 20 = 180
Or 4x - 20 = 180
Or 4x = 180 + 20
Or x = 200/4 = 50
Therefore, y = (3 x 50) - 20
= 150 - 20
= 130
b) Let the complementary angles be x and y.
(Y is the smaller angle and X is the bigger angle)
X = 2y + 15
Therefore, y + x = 90
Or 2y + y + 15 = 90
Or 3y + 15 = 90
Or 3y = 90 - 15
Or y = 75/3 = 25
Therefore, x = (2 x 25) + 15
= 50 + 15
= 65
c) Let the adjacent angles be n and x.
(N is the larger angle and X is the smaller angle)
N = 3x -20
Therefore, 3x + x - 20 = 120
Or 4x - 20 = 120
Or 4x = 120 + 20
Or x = 140/4 = 35
Therefore, n = (3 x 35) - 20
= 105 - 20
= 85
d) Complementary angle sum up to 90 degrees.
Therefore if they are vertical each angles sums up to 45 degrees.


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