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A flower arrangement has 8 carnations for every 4 roses. There are 14 carnations. How many roses are in the arrangement?
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<u>Given</u><u> info</u><u>:</u><u>-</u> In triangle (∆)ABC , in which ∠A = 2x, ∠B = x+15° and ∠C = 2x + 10°. Then find the value of x , also find the measure of each angles of a triangle.
<u>Explanation</u><u>:</u><u>-</u>
Let the angles be 2x, x+15 and 2x+10 respectively.
∵ Sum of the three angles of a triangle is 180°
∴ ∠A + ∠B + ∠C = 180° [Sum of ∠s of a ∆=180°]
→2x + x+15 + 2x+10 = 180°
→ 2x + x + 2x + 15 + 10 = 180°
→ 3x + 2x + 15 + 10 = 180°
→ 5x + 15 + 10 = 180°
→ 5x + 25 = 180°
→ 5x = 180°-25
→ 5x = 155°
→ x = 155°÷5 = 155/5 = 31.
Now, finding the measure of each angles of a ∆ABC by putting the original value of “x”.
∴ ∠A = 2x = 2(31) = 62°
∠B = x+15 = 31 + 15 = 46°
∠C = 2x + 10 = 2(31) + 10 = 62 + 10 = 72°.
