Question

For extra fun, groups of student in a class are tasked to create algebraic expression to satisfy the measures of the angles of their triangular picture frame project. If the measure of the angles are as follows:m∠A = 5x - 3, m∠C = 2x + 5, m∠E = 3x - 2, arrange the sides of the frame in increasing order.

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Answer 1

Explanation:

Sum of all angles of the triangle = 180

∠A + ∠C + ∠E = 180

5x - 3 + 2x +5 + 3x -2 = 180

Combine like terms

5x + 2x + 3x - 3 + 5 - 2 = 180

10x + 0 = 180

10x = 180

Divide both sides by 10

x = 180/10

x = 18

∠A = 5x - 3 = 5*18 - 3 = 90 - 3 = 87

∠C = 2x +5 = 2*18 + 5 = 36 + 5 = 41

∠E = 3x - 2 = 3*18 - 2 = 54 - 2 = 52

Side opposite to smallest angle is small

∠C is smallest. So, AE is smallest side

Next smallest is ∠E. So, AC is the next side

AE < AC < CE