Question

Of the three angles of a triangle, the second one is one third of the first and the third angle is 26 degrees more than the first angle. Find all the three angles of the triangle.​

Answer 1

Answer:

1angle= 66°

2 angle= 22°

3 angle=92°

Step-by-step explanation:

1 angle= x

2 angle=1/3x

3 angle = 26+x

using angle sum property,

x+1/3x+26+x=180

2x+1/3x+26=180

7x/3+26=180

7x/3=180-26

7x/3=154

7x=462

x=462/7

x=66

1angle= x= 66°

2 angle=1/3x=1/3×66=22°

3angle=26+x= 26+66=92°

Answer 2

${ \huge{ \underline{ \underline{ \sf{ \green{GivEn : }}}}}}$

• Of the three angles of a triangle, the second one is one third of the first and the third angle is 26° more than the first angle.

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• Three angles of the given triangle.

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

The 1st angle, 2nd angle and 3rd angle of the triangle be x°, y° and z° respectively.

Given that,

The second angle is 1/3 of the 1st angle.

Therefore,

⟶ y° = (1/3) × x

⟶ y° = x/3 ......................(eq(1)

Again, it’s given that

The 3rd angle is 26° more than the 1st angle.

z° = x + 26°.................eq(2)

According to the question :-

x ° + y° + z° = 180°........eq(4)

As we know that,

(The sum of 3 angles of a triangle is 180°)

Now, put y° = x/3 and z° = x + 26° in eq(4)

⟶ x° + (x/3) + (x +26°) = 180°

⟶ 2x° + (x/3) = 180° - 26°

⟶ 7x /3 = 154

⟶ x = 66°

Therefore,

1st angle will be = 66°

2nd angle will be = 66/3 = 22°

3rd angle will be = 66° + 26° = 92°