Question

24. In AABC, mZA = 3x + 1, mZB = 4x - 17, and
mZC = 5x - 20. Which type of triangle is AABC?
A) right
B) scalene
C) isosceles
D) equilateral

Answer 1

We know that the sum of the interior angles must be 180, so we have

$(3x+1)+(4x-17)+(5x-20)=180 \iff 12x-6=180 \iff 12x=216 \iff x=18$

So, the three angles are

$A=3x+1=3\cdot 18+1=55$

$B=4x-17=4\cdot 18-17=55$

And we can already conclude that the triangle is isosceles.