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The angles in a triangle are 3x – 7, 4x – 1, and 5x + 20.
Is the triangle right-angled?

1 Answer

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Answer:

Yes, the triangle is right-angled since one of the angles is 90°

Explanation:

The sum of the three angles of a triangle must add up to 180°

Here the three angles are 3x – 7, 4x – 1, and 5x + 20.

Adding them up gives

3x – 7 + 4x – 1 + 5x + 20 = 180

Grouping like terms:
3x + 4x + 5x - 7 - 1 + 20 = 180

12x + 12 = 180

12x = 180 - 12 = 168

x = 168/12 = 14

Substituting this value of x into each of the expressions:
3x – 7 = 3(14) - 7 = 42 - 7 = 35°

4x – 1 = 4(14) - 1 = 56 - 1 = 55°

5x + 20 = 5(14) + 20 = 70 + 20 = 90°

Since one of the angles is 90° it is indeed a right angled triangle

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