Question

The greatest angle of a triangle is 30 more than the smallest and the third angle is 15 less than the greatest find the angles of the triangle

Answer 1

Answer:

75,60,45

Step-by-step explanation:

let the smallest angle is X°

so greatest angle will be (X+30)°

and third angle Will be {(X+30)-15}°

sum of the all angles of any trangle is 180°

X+(X+30)+(X+15)= 180

3X +45= 180

3X = 135

X= 45°

Answer 2

Answer :

• ∠Ist = smallest angle = x = 45°

• ∠IInd = greatest angle = 75°

• And, ∠IIIrd = third angle = 60°

Given :

• The greatest angle of a triangle is 30 more than the smallest

• The third angle is 15 less than the greatest

To find :

• The angles of the triangle =?

Step-by-step explanation :

Let smallest angle = x

Then, greatest angle = (x +3)

And, third angle = (x+30)-15

We know that sum of all angles in triangle is 180°

∴ ∠1st + ∠2nd ∠3rd = 180°

⟹ x + ( x + 30) + (x + 30) - 15 = 180

⟹ x + x + 30 + x + 30 - 15 = 180

⟹ 3x + 60 - 15 = 180

⟹ 3x + 45 = 180

⟹ 3x = 180 - 45

⟹ 3x = 135

⟹ x = 135/3

⟹ x = 45

Hence,

∠Ist = smallest angle = x = 45°

∠IInd = greatest angle = x + 30

= 45 + 30 = 75°

And, ∠IIIrd = third angle = (x + 30) -15

= (45 + 30) - 15

= 75 - 15

= 60°.