NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.2 Question 3(ii)

NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.2 Question 3(ii)

Question:

Form the pair of linear equations for the following problems and find their solution by substitution method.

The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Given:

Let the two supplementary angles be x and y, where x is the larger angle and y is the smaller angle. The larger angle exceeds the smaller angle by 18 degrees.

To Find:

We need to find the values of the two supplementary angles x and y.

Formula:

Supplementary angles add up to 180 degrees. Therefore, x + y = 180

Solution:

We have two equations:

x + y = 180 ---(1)

x - y = 18 ---(2)

From equation (2), we can express x in terms of y:

x = y + 18 ---(3)

Substitute equation (3) into equation (1):

(y + 18) + y = 180

Simplify and solve for y:

2y + 18 = 180

2y = 180 - 18

2y = 162

y = 162 2 = 81

Substitute the value of y (81) back into equation (3) to find x:

x = 81 + 18 = 99

Result:

Therefore, the two supplementary angles are 99 degrees and 81 degrees.

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