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nata0808 [166]
3 years ago
7

The sum of the measures of the interior angles of a triangle is 180 °. The measure of the 1st angle is 15 ° less than the 2nd. T

he measure of the 3rd angle is 45 ° more than half of the second. Find the measure of e/ interior angle of the triangle.
Mathematics
1 answer:
DaniilM [7]3 years ago
3 0

1st angle (x): x - 15

2nd angle (y): x

3rd angle (z): \frac{1}{2}x + 45

The sum of the interior angles of a triangle equals 180°

1st angle + 2nd angle + 3rd angle = 180

x - 15 + x + \frac{1}{2}x + 45 = 180

2x + 30 + \frac{1}{2}x = 180 <em>(added like terms on left side)</em>

2x + \frac{1}{2}x = 150 <em>(subtracted 30 from both sides)</em>

4x + x = 300 <em>(multiplied all terms by 2 to eliminate the denominator)</em>

5x = 300 <em>(added like terms on left side)</em>

x = 60 <em>(divided by 5 on both sides)</em>

1st angle (x): x - 15 → (60) - 15 = 45

3rd angle (z): \frac{1}{2}x + 45 → \frac{1}{2}(60) + 45 → 30 + 45 = 75

Answer: 45°, 60°, 75°

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