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PLEASE HELP ME. ILL OFFER MANY POINTS
The middle angle in a triangle is 3 times the smallest angle. Twice the measure of the largest angle is the difference of 3 times the middle angle and twice the smallest angle. Find the measures of the angles.

small angle: middle angle: large angle:

Respuesta :

unicorn3125

Answer:

  small angle: 24° ;  middle angle: 72° ;  large angle: 84°

Step-by-step explanation:

x  - the smallest angle

3x  - the middle angle

2x   - twice the smallest angle

3·3x   -  3 times the middle angle

twice the measure of the largest angle (the difference of 3 times the middle angle and twice the smallest angle):  3·3x - 2x = 7x

7x÷2 = 3.5x  - the largest angle

The sum of angles in any triangle is 180°, so:

x + 3x + 3.5x = 180°

7.5x = 180°           {divide both sides by 7.5}

x = 24°

small angle:   x = 24°

middle angle:  3x = 3·24° = 72°

large angle:    3.5·24° = 84°

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