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The sum of interior angles in a triangle are 180 degrees. Angle B and C are congruent. Angle B is twenty less than angle A. Write and solve a system of equations using substitution. Write and solve a system to determine the measure of angles A, B, and C.

Respuesta :

MrRoyal

Answer:

[tex]A = \frac{220}{3}[/tex]

[tex]B = \frac{160}{3}[/tex]

[tex]C = \frac{160}{3}[/tex]

Step-by-step explanation:

Given

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

[tex]B = C[/tex]

[tex]B = A- 20[/tex]

Required

Solve for A, B and C

The equation binding A, B and C have been written out (above)

Substitute C for B in [tex]A + B + C = 180[/tex]

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

[tex]A + 2B = 180[/tex]

Substitute A - 20 for B

[tex]A + 2(A - 20) = 180[/tex]

[tex]A + 2A - 40 = 180[/tex]

[tex]3A - 40 = 180[/tex]

Solve for 3A

[tex]3A = 180 + 40[/tex]

[tex]3A = 220[/tex]

[tex]A = \frac{220}{3}[/tex]

Solve for B in [tex]B = A- 20[/tex]

[tex]B = \frac{220}{3} - 20[/tex]

[tex]B = \frac{220 - 60}{3}[/tex]

[tex]B = \frac{160}{3}[/tex]

Recall that [tex]B = C[/tex]

[tex]C = \frac{160}{3}[/tex]

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