Question

In the given figure, POQ is a straight line. Find x​

Answer 1

$\implies\tt{ 3x + 2 \degree + 7x - 12 \degree = 180 \degree\sf \purple{(linear \: pair)}} \\ \implies\tt{10x - 10 = 180 \degree} \\ \implies\tt{10x = (180 + 10) \degree} \\ \implies\tt{10x = 190 \degree} \\ \implies\tt{x = \frac{190}{10} } \\ \ \therefore \tt \purple{x = 19 \degree}$

$\bf \pink{Putting \: the \: value \: of \: x} \\ \tt{3x + 2 \implies3 \times 19 + 2 = 57 + 2 \implies59 \degree} \\ \tt{7x - 12 \implies7 \times 19 - 12 = 133 - 12 \implies121 \degree}$

Answer 2

$\huge\tt{Answer:-}$

$\bf{Given:-}$

• Angle POR = $({3x + 2}^{\degree})$.
• Angle ROQ = $({7x - 12}^{\degree} )$.
• Line POQ = Straight Angle = $( {180}^{\degree})$.

As per the diagram in the attachment, (see Question),

We can tell that:-

• $\sf{ \angle POQ = \angle POR + \angle ROQ}$ $\sf{...({Eq}^{n} \ N}$ - Let)

From that Eqⁿ N,

$(3x + {2}^{\degree}) + (7x - {12}^{\degree}) = {180}^{\degree}$

(Substituting the values.)

$\implies 3x + {2}^{\degree} + 7x - {12}^{\degree} = {180}^{\degree}$

$\implies 10x - {10}^{\degree} = {180}^{\degree}$

(Adding the like terms.)

$\implies 10x = {180}^{\degree} + {10}^{\degree} = {190}^{\degree}$

$\implies \cancel{10x} = \cancel{{190}^{\degree}}$

$\boxed{\implies x = {19}^{\degree}}$ $...(Ans.)$

______________...

$\huge\tt{Required:-}$

The value of x here is 19°.

_________...

$\huge\tt{Verification:-}$

Refer to the previous answer by @Blossomfairy.