Question

the measure of one angle of a triangle is 140° find out the other two angles if there difference is 20°​

Answer 1

Answer:

30 and 10 deg

Step-by-step explanation:

sum of three angles is 180deg

if one angle is 140 means sum of other two angles is 180-140= 40

let second angle be x and third be y

difference between x and y is 20

x-y= 20

x+y= 40

adding two equations we get2x = 60

x= 60/2= 30

third angle is 40-30= 10

Answer 2

$\large\underline{\sf{Solution-}}$

Let assume that the required triangle be ABC such that ∠A = 140°.

As it is given that, the other two angles differ by 20°

Let assume that ∠B = x

So, ∠C = x + 20

We know,

Sum of all interior angles of a triangle is 180°.

So, ∠A + ∠B + ∠C = 180°

$\rm \: 140 \degree+ x + x + 20\degree = 180\degree$

$\rm \: 160\degree + 2x = 180\degree$

$\rm \: 2x = 180\degree - 160\degree$

$\rm \: 2x = 20\degree$

$\rm\implies \:x = 10\degree$

So,

$\begin{gathered}\begin{gathered}\bf\: \rm\implies \:\begin{cases} &\sf{ \angle \: B \: = \: 10\degree} \\ \\ &\sf{ \angle \: C = 10 + 20 = 30\degree} \end{cases}\end{gathered}\end{gathered}$

$\rule{190pt}{2pt}$

Additional Information :-

1. The exterior angle of a triangle is equals to sum of interior opposite angles.

2. The sum of exterior angles of a triangle is 360°.

3. The sum of any two sides of a triangle is greater than third side.