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 abc
1. m∠a is six less than seven times x
2. m∠b is five less than three times x
3. m∠c is five less than four times x
We 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 - 5
Substitute 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 = 14
Substitute 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
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