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

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.

To find :

• Three angles of a triangle.

Solution :

Consider,

• The 1st angle of the triangle = x°
• The 2nd angle of the triangle = y°
• The 3rd angle of the triangle = z°

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

→ y° = (1/3) × x

→ y° = x/3 ......................(i)

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

→ z° = x + 26°.................(ii)

✪ We know, the sum of 3 angles of a triangle is 180°.

Therefore,

x ° + y° + z° = 180°

→ x° + (x/3) + (x +26°) = 180°

→ 2x° + (x/3) = 180° - 26°

→ 7x /3 = 154

→ x = 66°

• 1st angle = 66°
• 2nd angle = 66/3 = 22°
• 3rd angle = 66° + 26° = 92°

Answer 2

Answer:

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