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

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Let the angles be x and y

So, x+y=180 ∘ −(1) x=y+18 ⇒y+18+y=180 ∘ ∴y=81;x=99 ∘

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The larger of two supplementary angles exceeds the smaller by 18 degrees Find x and y...

Free solutions for NCERT Solutions - Mathematics , Class 10 Chapter 4 - Pair of Linear Equations in Two Variables Pair of Linear Equations in Two Variables - Exercise 3.3 question 6. These explanations are written by Lido teacher so that you easily understand even the most difficult concepts

NCERT Solutions Class 10 Mathematics Solutions for Pair of Linear Equations in Two Variables - Exercise 3.3 in Chapter 3 - Pair of Linear Equations in Two Variables

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Answer:

Let the larger angle be xo and smaller angle be yo.

We know that the sum of two supplementary pair of angles is always 180o.

According to the question,

x + y = 180o……………. (1)

x – y = 18o ……………..(2)

From (1), we get x = 180o – y …………. (3)

Substituting (3) in (2), we get

180o – y – y =18o 162o = 2y y = 81o ………….. (4)

Using the value of y in (3), we get

x = 180o – 81o = 99o

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The larger of two supplementary angles exceeds smaller by

Ex 3.3, 3 Form the pair of linear equations for the following problems and find their solution by substitution method. (ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them. Let Larger angle be x & Smaller angle be y Given that Larger ang

Ex 3.3, 3 (ii) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables (Term 1)

Last updated at March 16, 2023 by Teachoo

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Ex 3.3, 3 Form the pair of linear equations for the following problems and find their solution by substitution method. (ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them. Let Larger angle be x & Smaller angle be y Given that Larger angle exceeds Smaller angle by 18° x – y = 18 Also both angles are supplementary Sum of both angles = 180° x + y = 180 Thus, our equations are x – y = 18 …(1) x + y = 180 …(2) From (1) x – y = 18 x = 18 + y Substituting x in (2) x + y = 180 (18 + y) + y = 180 18 + y + y = 180 18 + 2y = 180 2y = 180 – 18 2y = 162 y = 162/2 = 81 Putting y = 81 in (1) x – y = 18 x – 81 = 18 x = 18 + 81 x = 99 Hence, x = 99 and y = 81 Thus, Larger Angle = x = 99° Smaller Angle = y = 81°

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