Question

The angles of AABC measure as follows:

mA = (4x - 10)°
m/B = (2x + 10)°
m/C= (5x-40)°
Solve for x, find the angle measures, then order the sides from shortest
to longest.
When you write your sides, they must be in alphabetical order.

Answer 1

AC , AB , BC

Explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles, equate to 180 and solve for x

4x - 10 + 2x + 10 + 5x - 40 = 180 ( collect like terms on left side )

11x - 40 = 180 ( add 40 to both sides )

11x = 220 ( divide both sides by 11 )

x = 20

Then

∠ A = 4x - 10 = 4(20) - 10 = 80 - 10 = 70°

∠ B = 2x + 10 = 2(20) + 10 = 40 + 10 = 50°

∠ C = 5x - 40 = 5(20) - 40 = 100 - 40 = 60°

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In any triangle

• the side opposite the largest angle is the longest side

• te side opposite the smallest angle is the shortest side

AC is opposite ∠ B = 50° ← shortest side

BC is opposite ∠ A = 70° ← longest side

The sides from shortest to longest : AC , AB , BC