Question

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Answer 1

x = 9

Explanation:

Answer 2

To Find the value of x and all angles :

We know that,

• Sum of all angles of a triangle = 180°.

⠀

Therefore,

`{ \longrightarrow \sf \qquad \angle1 + \angle2 + \angle3= 180 {}^( \circ) }`

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

⠀

Adding like terms we get :

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

`{ \longrightarrow \sf \qquad 21x+ ( - 9) {}^( \circ)= 180 {}^( \circ) }`

`{ \longrightarrow \sf \qquad 21x = 180 {}^( \circ) } \sf+ \: 9 {}^( \circ)`

`{ \longrightarrow \sf \qquad 21x = 189 {}^( \circ)}`

`{ \longrightarrow \sf \qquad x = \frac{189 {}^( \circ)}{21} }`

`{ \longrightarrow { \pmb{\bf \qquad x = 9 {}^( \circ)}}}`

⠀

Therefore,

`\longrightarrow \: \sf \qquad \angle1 = (13x + 2) {}^( \circ)`

`\longrightarrow \: \sf \qquad \angle1 = (13.9 + 2) {}^( \circ)`

`\longrightarrow \: \sf \qquad \angle1 = (117 + 2) {}^( \circ)`

`\longrightarrow \: \bf \qquad \angle1 = 119 {}^( \circ)`

⠀

`\longrightarrow \: \sf \qquad \angle2 = (5x - 7) {}^( \circ)`

`\longrightarrow \: \sf \qquad \angle2 = (5.9 - 7) {}^( \circ)`

`\longrightarrow \: \sf \qquad \angle2 = (45 - 7) {}^( \circ)`

`\longrightarrow \: \bf \qquad \angle2 = 38 {}^( \circ)`

⠀

`\longrightarrow \: \sf \qquad \angle3 = (3x - 4) {}^( \circ)`

`\longrightarrow \: \sf \qquad \angle3 = (3.9 - 4) {}^( \circ)`

`\longrightarrow \: \sf \qquad \angle3 = (27 - 4) {}^( \circ)`

`\longrightarrow \: \bf \qquad \angle3 = 23 {}^( \circ)`