In ΔABC, 2∠A = 3∠B = 6∠C. What is the value of the largest angle among these three angles?

90°

\(\angle\)A + \(\angle\)B + \(\angle\)C = 180

\(\angle\)A + \(\frac{2}{3}\)\(\angle\)A + \(\frac{1}{3}\)\(\angle\)A = 180

= (1 + \(\frac{2}{3}\) + \(\frac{1}{3}\))\(\angle\)A = 180

= 2\(\angle\)A = 180

= \(\angle\)A = 90

= \(\angle\)B = 60

= \(\angle\)C = 30

= Therefore, \(\angle\)A = \({90}^\circ\) is the value of the largest angle among these three angles.