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A triangle is such that the largest angle is 7 times the smallest angle. The third angle is 15 less than the largest angle. Find the measure of each angle.

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Answer:

The smallest angle measures 13°, the largest angle measures 91° and the third angle measures 76°

Step-by-step explanation:

Let's recall that the interior angles of a triangle add up to 180°, therefore we have:

Smallest angle = x

Largest angle = 7x

Third angle = 7x - 15

Now, we can solve for x, using the following equation:

x + 7x + 7x - 15 = 180

15x = 180 + 15

15x = 195

x = 195/15

x = 13 ⇒ 7x = 91 ⇒ 7x - 15 = 76

The smallest angle measures 13°, the largest angle measures 91° and the third angle measures 76°

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