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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Answers
Given : measure of the angle of triangular picture frame
m∠A = 5x - 3, m∠C = 2x + 5, m∠E = 3x - 2
To Find : , arrange the sides of the frame in increasing order.
Solution:
m∠A = 5x - 3, m∠C = 2x + 5, m∠E = 3x - 2
m∠A + m∠C + m∠E = 180°
=> 5x - 3 + 2x + 5 + 3x - 2 = 180°
=> 10x = 180°
=> x = 18°
m∠A = 5(18) - 3 = 87°
m∠C = 2(18) + 5 = 41°
m∠E = 3(18) - 2 = 52°
41° < 52° < 87°
=> m∠C < m∠E < m∠A
sides opposites to angles will be in the same order as angles
=> AE < AC < CE
the sides of the frame in increasing order.
AE , AC and CE
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To solve for x
(5×-3) + (2×+5) + (3×-2)=180
5×+2×3×-3+5-2=180
10×-5+5=180
10×180
×=180
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