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Select all the true statements. Triangle A B C where the measure of angle A is 2 x plus 1 degree, angle B is x degrees, and angle C is x plus 15 degrees. Group of answer choices m∠C = 56 From smallest to largest: ∠B, ∠C, ∠A m∠A = 99 x = 49 (4x + 16) = 180

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MrRoyal

Answer:

[tex]B= 41[/tex]; [tex]C = 56[/tex]; [tex]A = 83[/tex]

Step-by-step explanation:

Given

[tex]A = 2x + 1[/tex]

[tex]B = x[/tex]

[tex]C = x + 15[/tex]

Required

Arrange the angles from smallest to largest

First, we need to determine the value of x.

Since, it is a triangle:

[tex]A + B + C = 180[/tex]

Substitute values for A, B and C

[tex]2x + 1+ x + x + 15 = 180[/tex]

Collect Like Terms

[tex]2x + x + x = 180 - 15 -1[/tex]

[tex]4x = 164[/tex]

Solve for x

[tex]x= 164/4[/tex]

[tex]x= 41[/tex]

Solve for A, B and C

[tex]A = 2x + 1[/tex]

[tex]A = 2 * 41 + 1[/tex]

[tex]A = 82 + 1[/tex]

[tex]A = 83[/tex]

[tex]B = x[/tex]

[tex]B= 41[/tex]

[tex]C = x + 15[/tex]

[tex]C = 41 + 15[/tex]

[tex]C = 56[/tex]

From Smallest to Largest, we have:

[tex]B= 41[/tex]; [tex]C = 56[/tex]; [tex]A = 83[/tex]

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