Two angles are complementary. The larger angle is 3 ° less than twice the measure of the smaller angle. Find the measure of each angle.

Given: Two angles which are complementary. Let the larger of the two complementary angles be ' y ' and the smaller angle be ' x '. x + y = 90 ° (Sum of two complementary angles is 90 ° ) . . . ( I ) And, y = 2 x - 3 ° . . . ( II ) Substituting the value of y from ( II ) in ( I ) , we get ⇒ x + ( 2 x - 3 ° ) = 90 ° ⇒ 3 x - 3 ° = 90 ° ⇒ 3 x = 90 ° + 3 ° ⇒ 3 x = 93 ° ⇒ x = 31 ° Substitute x = 31 ° in ( II ) y = 2 × 31 ° - 3 ° = 62 ° - 3 ° = 59 ° Therefore, measure of the larger angle is 59 ° and the measure of the smaller angle is 31 ° .

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The sum of a two digit number and the number obtained by reversing the digits is $66$ . If the digits of the number differ by $2$ , find the number. How many such numbers are there?

Important Questions on Pair of Linear Equations

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Mathematics Class 10>Chapter 4 - Pair of Linear Equations>Exercise>Q 3

The larger of two supplementary angles exceeds the smaller by $18 °$ . Find the angles.

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Mathematics Class 10>Chapter 4 - Pair of Linear Equations>Exercise>Q 4

The taxi charges in Hyderabad are fixed, along with the charge for the distance covered. Upto first

3 km

you will be charged a certain minimum amount. From there onwards you have to pay additionally for every kilometer travelled. For the first

10 km

, the charge paid is

₹ 166

. For a journey of

15 km

. the charge paid is

1

.
What are the fixed charges and charge per

km

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Mathematics Class 10>Chapter 4 - Pair of Linear Equations>Exercise>Q 4

The taxi charges in Hyderabad are fixed, along with the charge for the distance covered. Upto first $3 km$ you will be charged a certain minimum amount. From there onwards you have to pay additionally for every kilometer travelled. For the first $10 km$ , the charge paid is $₹ 166$ . For a journey of $15 km$ . the charge paid is $₹ 256$ .

How much does a person have to pay for travelling a distance of $25 km$ ?

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Mathematics Class 10>Chapter 4 - Pair of Linear Equations>Exercise>Q 5

A fraction will be equal to

\frac{4}{5}

1

is added to both numerator and denominator. If, however,

5

is subtracted from both numerator and denominator, the fraction will be equal to

\frac{1}{2}

. What is the fraction?

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Mathematics Class 10>Chapter 4 - Pair of Linear Equations>Exercise>Q 6

Places

A

and

B

are

100 km

apart on a highway. One car starts from

A

and another from

B

at the same time at different speeds. If the cars travel in the same direction, they meet in

5

hours. If they travel towards each other, they meet in

1

hour. What are the speeds of the two cars?

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Mathematics Class 10>Chapter 4 - Pair of Linear Equations>Exercise>Q 7

Two angles are complementary. The larger angle is

x - 4 = 2 \Rightarrow x = 6

less than twice the measure of the smaller angle. Find the measure of each angle.

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Mathematics Class 10>Chapter 4 - Pair of Linear Equations>Exercise>Q 8

A dictionary has a total of

1382

pages. It is broken up into two parts. The second part of the book has

64

pages more than the first part. How many pages are in each part of the book?

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Mathematics Class 10>Chapter 4 - Pair of Linear Equations>Exercise>Q 9

A chemist has two solutions of hydrochloric acid in stock. One is

50 %

solution and the other is

80 %

solution. How much of each should be used to obtain

100 ml

of a

68 %

solution.

The sum of a two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?

Important Questions on Pair of Linear Equations

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The sum of a two digit number and the number obtained by reversing the digits is $66$ . If the digits of the number differ by $2$ , find the number. How many such numbers are there?