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Answer:

x = 9

Step-by-step explanation:

To Find the value of x and all angles :

We know that,

⠀

Therefore,

[tex]{ \longrightarrow \sf \qquad \angle1 + \angle2 + \angle3= 180 {}^{ \circ} }[/tex]

[tex]{ \longrightarrow \sf \qquad (13x + 2) {}^{ \circ} + (5x - 7){}^{ \circ}+ (3x - 4) {}^{ \circ} = 180 {}^{ \circ} }[/tex]

⠀

Adding like terms we get :

[tex]{ \longrightarrow \sf \qquad (13x +5x + 3x) + { \bigg[2 + ( - 7) + ( - 4) \bigg]}^{ \circ}= 180 {}^{ \circ} }[/tex]

[tex]{ \longrightarrow \sf \qquad 21x+ ( - 9) {}^{ \circ}= 180 {}^{ \circ} }[/tex]

[tex]{ \longrightarrow \sf \qquad 21x = 180 {}^{ \circ} } \sf+ \: 9 {}^{ \circ}[/tex]

[tex]{ \longrightarrow \sf \qquad 21x = 189 {}^{ \circ}}[/tex]

[tex]{ \longrightarrow \sf \qquad x = \dfrac{189 {}^{ \circ}}{21} }[/tex]

[tex]{ \longrightarrow { \pmb{\bf \qquad x = 9 {}^{ \circ}}}}[/tex]

⠀

Therefore,

[tex] \longrightarrow \: \sf \qquad \angle1 = (13x + 2) {}^{ \circ}[/tex]

[tex]\longrightarrow \: \sf \qquad \angle1 = (13.9 + 2) {}^{ \circ}[/tex]

[tex]\longrightarrow \: \sf \qquad \angle1 = (117 + 2) {}^{ \circ}[/tex]

[tex]\longrightarrow \: \bf \qquad \angle1 = 119 {}^{ \circ}[/tex]

⠀

[tex]\longrightarrow \: \sf \qquad \angle2 = (5x - 7) {}^{ \circ}[/tex]

[tex]\longrightarrow \: \sf \qquad \angle2 = (5.9 - 7) {}^{ \circ}[/tex]

[tex]\longrightarrow \: \sf \qquad \angle2 = (45 - 7) {}^{ \circ}[/tex]

[tex]\longrightarrow \: \bf \qquad \angle2 = 38 {}^{ \circ}[/tex]

⠀

[tex]\longrightarrow \: \sf \qquad \angle3 = (3x - 4) {}^{ \circ}[/tex]

[tex]\longrightarrow \: \sf \qquad \angle3 = (3.9 - 4) {}^{ \circ}[/tex]

[tex]\longrightarrow \: \sf \qquad \angle3 = (27 - 4) {}^{ \circ}[/tex]

[tex]\longrightarrow \: \bf \qquad \angle3 = 23 {}^{ \circ}[/tex]

Please. I NEED NOW!!

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