Answer:
[tex]x = 15 $^{\circ}$ ; z = 74$^{\circ}$[/tex]
Step-by-step explanation:
First, combine all like terms. Like terms are terms that have the same amount of the same variables:
[tex]m$\angle$(5x - 1) + m$\angle$(7x + 1) = 180$^{\circ}$\\\\[/tex]
[tex]m$\angle$(5x + 7x) + (1 - 1) = 180$^{\circ}$[/tex]
[tex]12x + 0 = 180$^{\circ}$[/tex]
Next, isolate the variable, x. Divide 12 from both sides of the equation:
[tex]12x = 180\\\frac{12x}{12} = \frac{180}{12}\\ x = \frac{180}{12}\\ x = 15 $^{\circ}$[/tex]
Next, plug in 15 for x in one of the given expressions. If you choose the right one (7x + 1), you will solve using the straight angle theorem. If you choose the bottom one (5x - 1), you will solve using the vertical angle postulate. Both will give you the same answer for x.
Firstly, if you want to solve using the straight angle theorem. The straight angle theorem is defined that all straight angles are 180 degrees. Solve using the straight angle theorem. Set both angle measurements equal to 180°:
[tex](z) + (7x + 1) = 180[/tex]
Plug in 15 for x and solve for the parenthesis:
[tex]z + 7(15) + 1 = 180 $^{\circ}$\\[/tex]
First, multiply 7 with 15:
[tex]z + (7 * 15) + 1 = 180 $^{\circ}$\\z +105 + 1 = 180$^{\circ}$\\[/tex]
Next, simplify by combining like terms:
[tex]z + (105 + 1) = 180 $^{\circ}$\\z + 106 = 180$^{\circ}$[/tex]
Next, isolate the variable, z, by subtracting 106 from both sides of the equation:
[tex]z + 106 = 180 $^{\circ}$\\z + 106 (-106) = 180 (-106)\\z = 180 - 106\\z = 74$^{\circ}$[/tex]
Your answer:
[tex]x = 15 $^{\circ}$ ; z = 74$^{\circ}$[/tex]
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