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