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find the value of x in the diagram below

Find The Value Of X In The Diagram Below class=

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[tex]\qquad \qquad\huge \underline{\boxed{\sf Answer}}[/tex]

In the given diagram, The shown angles form Linear pair. And according to that property the sum of measures of the two Angles equals to 180°

Now, let's use the equation to solve for x ~

[tex]\qquad \sf  \dashrightarrow \:( 13x + 6) + (29x + 6) = 180 \degree[/tex]

[tex]\qquad \sf  \dashrightarrow \: 13x + 6 + 29x + 6= 180 \degree[/tex]

[tex]\qquad \sf  \dashrightarrow \: 13x + 29x + 6 + 6= 180 \degree[/tex]

[tex]\qquad \sf  \dashrightarrow \: 42x + 12= 180 \degree[/tex]

[tex]\qquad \sf  \dashrightarrow \: 42x = 180 \degree - 12 \degree[/tex]

[tex]\qquad \sf  \dashrightarrow \: 42x = 168 \degree [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 168 \degree \div 42[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 4 \degree[/tex]

[tex]\fbox \colorbox{black}{ \colorbox{white}{x} \:  \:  \:   \:  \:  \:  \: \: \colorbox{white}{=}  \:  \:  \:  \:  \:   + \colorbox{white}{4 \degree}}[/tex]

The angles marked in the given diagram are forming a linear pair of angles, Which means that their sum will be 180°...~

  • ∠1 = 13x+6
  • ∠2 = 29x+6

[tex]\colorbox{lightyellow}{(13x + 6) + (29x + 6) = 180 \degree}[/tex]

Solve the equation for x ~

[tex] \rm \: 42x + 12 = 180[/tex]

[tex] \rm \: 42x = 180 - 12[/tex]

[tex] \rm \: 42x = 168[/tex]

[tex] \rm \: 42x \div 42 = 168 \div 42[/tex]

[tex] \rm \: x = 4[/tex]

Now,

[tex]\large{|\underline{\mathtt{\red{1}\blue{ ^{st} }\orange{ \: }\pink{a}\blue{n}\purple{g}\green{l}\red{e}\orange{ \curvearrowright}}}}[/tex]

[tex] \sf \: 13x + 6 \\ \sf \: 13 \times 4 + 6 \\ \sf \: ∠1 = 58 \degree[/tex]

[tex]\large{|\underline{\mathtt{\red{2}\blue{ ^{nd} }\orange{ \: }\pink{a}\blue{n}\purple{g}\green{l}\red{e}\orange{ \curvearrowright}}}}[/tex]

[tex] \sf \: 29x + 6 \\ \sf \: 29 \times 4 + 6 \\ \sf \: ∠2 = 122 \degree[/tex]

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