The sides of ABC are 24°, 50°, and 126°.
Given that
The angles of the triangle are as follows.
∠A = 8x – 2, ∠B = 2x – 8, and ∠C = 94 – 4x.
We have to determine
The sides of ABC are in order from shortest to longest.
According to the question
The sum of all the three angles is the triangle is equal to 180 degrees.
The angles of the triangle are as follows.
∠A = 8x – 2, ∠B = 2x – 8, and ∠C = 94 – 4x.
Then,
[tex]\rm \angle A + \angle B+ \angle C = 180\\\\ 8x-2+2x-8+94-4x=180\\\\6x = 180-94+8+2\\\\6x= 96\\\\x = \dfrac{96}{6}\\\\x = 16[/tex]
The value of x is 16.
Therefore,
The measure of ∠A = 8x-2 = 8(16)-2 = 128-2 = 126 degree
The measure of ∠B = 2x-8 = 2(16)-8 = 32-8 = 24 degree
The measure of ∠C = 94-4x = 94-4(16) = 94-64 = 50 degree
Hence, The sides of ABC are 24°, 50°, and 126°.
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