Question 1

Find the value of x in the diagram below

Question 2

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

$\colorbox{lightyellow}{(13x + 6) + (29x + 6) = 180 \degree}$

Solve the equation for x ~

$\rm \: 42x + 12 = 180$

$\rm \: 42x = 180 - 12$

$\rm \: 42x = 168$

$\rm \: 42x / 42 = 168 / 42$

$\rm \: x = 4$

$\large{|\underline{\mathtt{\red{1}\blue{ ^(st) }\orange{ \: }\pink{a}\blue{n}\purple{g}\green{l}\red{e}\orange{ \curvearrowright}}}}$

$\sf \: 13x + 6 \\ \sf \: 13 * 4 + 6 \\ \sf \: ∠1 = 58 \degree$

$\large{|\underline{\mathtt{\red{2}\blue{ ^(nd) }\orange{ \: }\pink{a}\blue{n}\purple{g}\green{l}\red{e}\orange{ \curvearrowright}}}}$

$\sf \: 29x + 6 \\ \sf \: 29 * 4 + 6 \\ \sf \: ∠2 = 122 \degree$

Question 3

$\qquad \qquad\huge \underline{\boxed{\sf Answer}}$

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 ~

$\qquad \sf  \dashrightarrow \:( 13x + 6) + (29x + 6) = 180 \degree$

$\qquad \sf  \dashrightarrow \: 13x + 6 + 29x + 6= 180 \degree$

$\qquad \sf  \dashrightarrow \: 13x + 29x + 6 + 6= 180 \degree$

$\qquad \sf  \dashrightarrow \: 42x + 12= 180 \degree$

$\qquad \sf  \dashrightarrow \: 42x = 180 \degree - 12 \degree$

$\qquad \sf  \dashrightarrow \: 42x = 168 \degree$

$\qquad \sf  \dashrightarrow \: x = 168 \degree / 42$

$\qquad \sf  \dashrightarrow \: x = 4 \degree$

$\fbox \colorbox{black}{ \colorbox{white}{x} \:  \:  \:   \:  \:  \:  \: \: \colorbox{white}{=}  \:  \:  \:  \:  \:   + \colorbox{white}{4 \degree}}$

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