10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

If the angles of a triangle are x, y and \[40{}^\circ \] and the difference between the two angles x and y is \[30{}^\circ \]. Then, the value of x and y is \[85{}^\circ \]and \[55{}^\circ \]respectively.

A) True

B) False

C) Can't say

D) Partially true/false

Correct Answer: A

Solution :

Given that, x, y and \[40{}^\circ \]are the angles of a triangle.

\[\therefore \,\,\,\,\,x+y+40{}^\circ =180{}^\circ \]

[since, the sum of all the angles of a triangle is \[180{}^\circ \]]

\[\Rightarrow \,\,\,\,x+y=140{}^\circ \] (i)

Also, \[x-y=30{}^\circ \] (ii)

On adding Eqs. (i) and (ii), we get

\[2x=170{}^\circ \]

\[\Rightarrow \,\,\,x=85{}^\circ \]

On putting \[x\text{ }=\text{ }85{}^\circ \]in Eq. (i), we get

\[85{}^\circ +y=140{}^\circ \]

\[\Rightarrow \,\,\,\,\,\,\,\,y=55{}^\circ \]

Hence, the required values of x and y are \[85{}^\circ \]and \[55{}^\circ \], respectively.