Question

5. Two angles of triangle are equal, and the third angle is greater than each of these angles by 30°
Find all the angles of the triangle
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Answer 1

Given :

• Two angles of triangle are equal
• Third angle is greater than each of these by 30°

To find :

• All the angles of triangle

Solution :

Let,

• Two equal angles = x° each
• Third angle = (x + 30)°

Using formula,

• Sum of angles of a polygon = (2n - 4) × 90°

where,

• n is the number of sides

Triangle has 3 sides, 3 angles.

⠀⠀⠀⇒ x° + x° + x° + 30° = (2n - 4) × 90°

⠀⠀⠀⇒ 3x° + 30° = ((2 × 3) - 4) × 90°

⠀⠀⠀⇒ 3x° + 30° = (6 - 4) × 90°

⠀⠀⠀⇒ 3x° + 30° = 2 × 90°

⠀⠀⠀⇒ 3x° + 30° = 180°

⠀⠀⠀⇒ 3x° = 180° - 30°

⠀⠀⠀⇒ 3x° = 150°

⠀⠀⠀⇒ x = 150°/30°

⠀⠀⠀⇒ x = 50°

The value of x = 50°

Therefore, the three angles of triangle :-

• First angle = x = 50°
• Second angle = x = 50°
• Third angle = x + 30° = 50° + 30° = 80°

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Verification :-

Add all the angles of triangle if their sum is equal to 180° then the values are right.

⠀⠀⠀⇒ 50° + 50° + 80°

⠀⠀⠀⇒ 180°

Sum of angles of triangle = 180°

Hence, verified.