# intermediate algebra

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A triangle is such that the largest angle is 11 times the smallest angle. The third angle is 27° less than the largest angle. Find the measure of each angle. (Enter solutions from smallest to largest.)

• intermediate algebra -

The largest angle = 11 * the smallest angle

The third angle = The largest angle - 27 ° = 11 * the smallest angle - 27 °

The angles of a triangle always sum to 180 °

The smallest angle + The largest angle + The third angle = 180 °

The smallest angle + 11 * the smallest angle + 11 * the smallest angle -27 ° = 180°

23 * the smallest angle - 27 ° = 180 °

23 * the smallest angle = 180 ° + 27 °

23 * the smallest angle = 207 ° Divide both sides by 23

The smallest angle = 207 ° / 23

The smallest angle = 9 °

The largest angle = 11 * the smallest angle

The largest angle = 11 * 9 °

The largest angle = 99 °

The third angle = The largest angle - 27 °

The third angle = 99 ° - 27 °

The third angle = 72 °

72 ° + 99 ° + 9 ° = 180 °