Question

The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is 10°. Find the three angles.​

Answer 1

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The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is 10°. Find the three angles.

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$\huge\boxed{\blue{Given :}}$

➣ The Angles of a triangle are arranged in ascending order of magnitude

➣ The Difference between two consecutive angles = 10°

➣ Let the First angle of the triangle = x

➣ Let the Second angle of the triangle = x + 10°

➣ Let the third angle of the triangle = x + 10° + 10°

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➣ The three angles of a triangle

$\huge\boxed{\pink {Solution :}}$

➪ By using Angle Sum Property of triangle

➪ Sum of angles in a triangle = 180°

⇒ x + x + 10° + x + 10° + 10° = 180°

⇒ 3x + 30° = 180°

⇒ 3x = 180° - 30°

⇒ 3x = 150°

⇒ x = $\cancel\frac{150} {3}$

⇒ x = 50°

➣ First angle of the triangle = x = 50°

➣ Second angle of the triangle = x + 10° = 50° + 10° = 60°

➣ Third angle of the triangle = x + 10° + 10° = 50° + 10° + 10° = 70°

➦ So, the three angles of a triangle are 50°,60° and 70°

Answer 2

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The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is 10°. Find the three angles.

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1st angle be x

2nd angle be x+10°

3rd angle be x+20°

By triangle angle sum property

∠1+∠2+∠3=180°

x+x+10°+x+20°=180°

3x+30°=180°

3x=180°-30°

3x=150°

x=150°/3

x=50°

1st angle be x=50°

2nd angle be x+10°=50°+10°=60°

3rd angle be x+20°=50°+20°=70°

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