Question

(17) in triangle ABC, sum of measures of two angles is 60 and difference between them is 20, then find the
measures of all the angles of A ABC.​

Answer 1

Answer :-

Let the angles of triangle be x , y and z.

According to the question :-

x + y = 60

x - y = 20

By solving this linear equation -

➩ $\sf x + y = 60\: \: \: \: \: -i$

➩ $\sf x - y = 20 \: \: \: \: \: -ii$

Adding i and ii -

➩ $\sf x + \cancel{y} + x - \cancel{y} = 60 + 20$

➩ $\sf 2x = 80$

➩ $\sf x = \frac{80}{2}$

➩ $\boxed{\sf x = 40}$

Substituting the value in i

➩ $\sf x + y = 60$

➩ $\sf 40 + y = 60$

➩ $\sf y = 60 - 40$

➩ $\boxed{\sf y = 20}$

Now, we have two measures of anglesof triangle -

➩ x = 40°

➩ y = 20°

By angle sum property of traingle :-

➩ $\sf x + y + z = 180$

➩ $\sf 40 + 60 + z = 180$

➩ $\sf 100 + z = 180$

➩ $\sf z = 180 - 100$

➩ $\boxed{\sf z = 80}$

Hence, angles of triangle are 40° , 20° and 80°.