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ExitExam+ESSLCE Support: post #1469 — TG.ME

ExitExam+ESSLCE Support@tutorialpointeth · 2.7K subscribers Open in TelegramOpen

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August 4, 2024 2.9K 2

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[media post] 2.5K·Aug 4 📌Answer to Question #1️⃣👆 ✅️A triangle has angles in the ratio 2:3:5. What are the measures of the angles? 🔑To solve this question, we can set up an equation using the given ratio. And, we know that the sum of the three angles of a triangle is 180°. If we name the angles by the symbols: a, b and c. Then, a + b + c = 180° Given that a/b=2/3 and b/c=3/5, we get a= 2/3b and b= 3/5c, so, a=2/3(3/5c)=2/5c. Now, both a and b are expressed interms of c. So, In the equation a + b + c = 180° Replace a and b to get, 2/5c + 3/5c + c = 180° Which is one equation in one variable. multiply both sides by 5 to get rid of the denominator : 2c + 3c + 5c = 5×180 10c =900 c = 90 Then, b= 3/5c => b = 3/5(90) = 3×(90/5) = 3×18 = 54, and a = 2/3b = 2/3(54)= 36. ✅Check: 36 + 54 + 90 = 180. 📚OR🔑 Let x be the common multiplier for the ratio. The measures of the angles can be represented as 2x, 3x, and 5x. Since the sum of the angles in a triangle is 180 degrees, we can set up the equation: 2x + 3x + 5x = 180 Simplifying the equation: 10x = 180 Dividing both sides by 10: x = 18 Now we can find the measures of the angles: 2x = 2 × 18 = 36 degrees 3x = 3 × 18 = 54 degrees 5x = 5 × 18 = 90 degrees Therefore, the measures of the angles in the triangle are 36 degrees, 54 degrees, and 90 degrees. https://t.me/tutorialpointeth 2.7K·Aug 1

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