List the sides of ΔRST in ascending order (shortest to longest) if: m∠R = x+28°, m∠S = 2x+16°, and m∠T = x+12

Question

Mathematics

Maia Rosales

14 February, 15:37

List the sides of ΔRST in ascending order (shortest to longest) if: m∠R = x+28°, m∠S = 2x+16°, and m∠T = x+12

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Answers (1)

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Charity Booker · Answer 1

t, r, s

Step-by-step explanation:

The sum of angles is 180°, so you have ...

(x + 28) + (2x + 16) + (x + 12) = 180

4x + 56 = 180

4x = 124

x = 31

For this value of x, ...

2x+16 > x+28, so S is the largest angle and "s" is the longest side.

x + 12 < x + 28, so T is the smallest angle and "t" is the shortest side.

The sides, shortest to longest, are ... t = RS, r = ST, s = RT.