Find the 100th term in the sequence -3,-5,-7,-9... a.195 b.-201 c.201 d.-195
1 answer:
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1st angle (x): x - 15
2nd angle (y): x
3rd angle (z): x + 45
The sum of the interior angles of a triangle equals 180°
1st angle + 2nd angle + 3rd angle = 180
x - 15 + x + x + 45 = 180
2x + 30 + x = 180 <em>(added like terms on left side)</em>
2x + 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): x + 45 →
(60) + 45 → 30 + 45 = 75
Answer: 45°, 60°, 75°