Advertisements
Advertisements
Question
The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. Find x and y.
Solution
Given that x, y and 40° are the angles of a triangle.
∴ x + y + 40° = 180°
Since, the sum of all the angles of a triangle is 180°
⇒ x + y = 140° ......(i)
Also, x – y = 30° ......(ii)
On adding (i) and (ii), we get
2x = 170°
⇒ x = 85°
On putting x = 85° in (i), we get
85° + y = 140°
⇒ y = 55°
Hence, the required values of x and y are 85° and 55°, respectively.
APPEARS IN
RELATED QUESTIONS
Solve the following pair of linear equation by the elimination method and the substitution method:
x + y = 5 and 2x – 3y = 4
Solve the following pair of linear equation by the elimination method and the substitution method:
3x + 4y = 10 and 2x – 2y = 2
Solve the following pair of linear equation by the elimination method and the substitution method.
`x/2 + (2y)/3 = -1 and x - y /3 = 3`
Solve the following simultaneous equation.
x - 2y = -1 ; 2x - y = 7
By equating coefficients of variables, solve the following equation.
4x + y = 34 ; x + 4y = 16
If 52x + 65y = 183 and 65x + 52y = 168, then find x + y = ?
The sum of the two-digit number and the number obtained by interchanging the digits is 132. The digit in the ten’s place is 2 more than the digit in the unit’s place. Complete the activity to find the original number.
Activity: Let the digit in the unit’s place be y and the digit in the ten’s place be x.
∴ The number = 10x + y
∴ The number obtained by interchanging the digits = `square`
∴ The sum of the number and the number obtained by interchanging the digits = 132
∴ 10x + y + 10y + x = `square`
∴ x + y = `square` .....(i)
By second condition,
Digit in the ten’s place = digit in the unit’s place + 2
∴ x – y = 2 ......(ii)
Solving equations (i) and (ii)
∴ x = `square`, y = `square`
Ans: The original number = `square`
Difference between two numbers is 3. The sum of three times the bigger number and two times the smaller number is 19. Then find the numbers
The ratio of two numbers is 2:3. If 5 is added in each numbers, then the ratio becomes 5:7 find the numbers.
The ratio of two numbers is 2:3.
So, let the first number be 2x and the second number be `square`.
From the given condition,
`((2x) + square)/(square + square) = square/square`
`square (2x + square) = square (square + square)`
`square + square = square + square`
`square - square = square - square`
`- square = - square`
x = `square`
So, The first number = `2 xx square = square`
and, Second number = `3 xx square = square`
Hence, the two numbers are `square` and `square`
A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their places. Find the number.
