Answer:
[tex]A = 34\frac{1}{3}[/tex]
[tex]B = 72\frac{2}{3}[/tex]
[tex]C = 73[/tex]
Step-by-step explanation:
Given
Shape: Triangle
[tex]B = 4 + 2A[/tex]
[tex]C = 3A - 30[/tex]
Required
Solve for A, B and C
Since the shape is a triangle,
[tex]A + B +C = 180[/tex]
Substitute [tex]B = 4 + 2A[/tex] and [tex]C = 3A - 30[/tex] in [tex]A + B +C = 180[/tex]
[tex]A + 4 + 2A + 3A - 30 = 180[/tex]
Collect Like Terms
[tex]A + 2A + 3A = 180 + 30 - 4[/tex]
[tex]6A = 206[/tex]
Solve for A
[tex]A = 206/6[/tex]
[tex]A = 34\frac{1}{3}[/tex]
Substitute [tex]A = 34\frac{1}{3}[/tex] in [tex]B = 4 + 2A[/tex]
[tex]B = 4 + 2 * 34\frac{1}{3}[/tex]
[tex]B = 4 + 2 * \frac{103}{3}[/tex]
[tex]B = 4 + \frac{206}{3}[/tex]
[tex]B = \frac{12 + 206}{3}[/tex]
[tex]B = \frac{218}{3}[/tex]
[tex]B = 72\frac{2}{3}[/tex]
Substitute [tex]A = 34\frac{1}{3}[/tex] in [tex]C = 3A - 30[/tex]
[tex]C = 3 * 34\frac{1}{3} - 30[/tex]
[tex]C = 3 * \frac{103}{3} - 30[/tex]
[tex]C = 103 - 30[/tex]
[tex]C = 73[/tex]
