Answer:
<h3>
small angle: 24° ; middle angle: 72° ; large angle: 84°</h3>
Step-by-step explanation:
<u>x </u> - the smallest angle
<u>3x</u> - 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
<u>7x÷2 = 3.5x</u> - 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: <u>x = 24°</u>
middle angle: <u>3x = 3·24° = 72°</u>
large angle: <u>3.5·24° = 84°</u>
