[tex] \Large{\red{\boxed{ \sf x = 28}}} [/tex]
[tex] \\ [/tex]
[tex] \sf 89 + (5x - 8) + (3x + 4) + 51 = 360 \\ \\ \square \sf \: rewrite \: without \: the \: \: parentheses \\ \\ \sf89 + 5x - 8 + 3x + 4 + 51 = 360 \\ \\ \square \sf \: collect \: like \: terms \\ \\ \sf (5x + 3x) + (89 - 8 + 4 + 51) = 360 \\ \\ \square \: \sf \: simplify \: the \: equation \\ \\ \sf \: 8x + 136 = 360 \\ \\ \square \: \sf \: subtract \: 136 \: from \: both \: sides \: \\ \\ \sf 8x = 224 \\ \\ \square \: \sf \: divide \: both \: sides \: by \: 8 \\ \\ \sf \: x = \frac{224}{8} = \red{\boxed{ \sf \: 28}}[/tex]
Finally, determine the measure of the other angles thanks to the value of x:
[tex] \sf 5 \red{x} - 8 = 5 \red{(28)} - 8 = 140 - 8 = \boxed{ \sf 132} \\ \\ \sf 3\red{x} + 4 = 3 \red{(28)} + 4 = 84 + 4 = \boxed{ \sf \: 88}[/tex]
If we are right, the sum of the angles is equal to 360°. Let's check it out!
[tex] \sf 132^{ \circ} + 88 ^{ \circ} + 89 ^{ \circ} + 51 ^{ \circ} = 220 ^{ \circ} + 140^{\circ} = \boxed{ \boxed{ \sf360 ^{ \circ} }}[/tex]
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Answers & Comments
[tex] \Large{\red{\boxed{ \sf x = 28}}} [/tex]
[tex] \\ [/tex]
[tex] \sf 89 + (5x - 8) + (3x + 4) + 51 = 360 \\ \\ \square \sf \: rewrite \: without \: the \: \: parentheses \\ \\ \sf89 + 5x - 8 + 3x + 4 + 51 = 360 \\ \\ \square \sf \: collect \: like \: terms \\ \\ \sf (5x + 3x) + (89 - 8 + 4 + 51) = 360 \\ \\ \square \: \sf \: simplify \: the \: equation \\ \\ \sf \: 8x + 136 = 360 \\ \\ \square \: \sf \: subtract \: 136 \: from \: both \: sides \: \\ \\ \sf 8x = 224 \\ \\ \square \: \sf \: divide \: both \: sides \: by \: 8 \\ \\ \sf \: x = \frac{224}{8} = \red{\boxed{ \sf \: 28}}[/tex]
[tex] \\ [/tex]
Finally, determine the measure of the other angles thanks to the value of x:
[tex] \sf 5 \red{x} - 8 = 5 \red{(28)} - 8 = 140 - 8 = \boxed{ \sf 132} \\ \\ \sf 3\red{x} + 4 = 3 \red{(28)} + 4 = 84 + 4 = \boxed{ \sf \: 88}[/tex]
[tex] \\ [/tex]
If we are right, the sum of the angles is equal to 360°. Let's check it out!
[tex] \sf 132^{ \circ} + 88 ^{ \circ} + 89 ^{ \circ} + 51 ^{ \circ} = 220 ^{ \circ} + 140^{\circ} = \boxed{ \boxed{ \sf360 ^{ \circ} }}[/tex]