The value of x is 14 and m∠a is 92°, m∠b is 37° and m∠c is 51°Step-by-step explanation:In Δ abc1. m∠a is six less than seven times x2. m∠b is five less than three times x3. m∠c is five less than four times xWe need to find x and the measure of each angle∵ The sum of the measures of the interior angles in any triangle is 180°∴ m∠a + m∠b + m∠c = 180°∵ m∠a is 6 less than 7 times x∴ m∠a = 7x - 6∵ m∠b is 5 less than 3 times x∴ m∠b = 3x - 5∵ m∠c is 5 less than 4 times x∴ m∠c = 4x - 5Substitute the values of the angles in the rule above∴ 7x - 6 + 3x - 5 + 4x - 5 = 180- Add like terms in the left hand side∴ 14x - 16 = 180- Add 16 to both sides∴ 14x = 196- Divide both sides by 14∴ x = 14Substitute the value of x in each angle to find their measures∵ m∠a = 7x - 6∴ m∠a = 7(14) - 6∴ m∠a = 92°∵ m∠b = 3x - 5∴ m∠b = 3(14) - 5∴ m∠b = 37°∵ m∠c = 4x - 5∴ m∠c = 4(14) - 5∴ m∠c = 51°The value of x is 14 and m∠a is 92°, m∠b is 37° and m∠c is 51°Learn more:You can learn more about angles in brainly.com/question/10483199#LearnwithBrainly