Question

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Answer 1

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION\: \: } \mid}}}}}$

$\underline{ \mathfrak{ \: \: Given, \: \: }} \\ \\ \: \: \: \: \: \: \huge{ \text{ \red{a = 30 \degree}}} \\ \\ \underline{ \mathfrak{ \: \: To \: \: find : \: }} \\ \\ \huge{ \text{ \red{ The value of x = ? \: }}}$

$\underline{ \mathfrak{ \: \: We \: \: know \: \: that, \: \: }} \\ \\ \red{ \text{</p><p>The sum of the three angles of a triangle}} \\ \red{ \text{ is equal to 180 \degree}.}$

$\mathfrak{So,} \\ \: \: \: \: \: \: \underline{ \text{ \: In the diagram, \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \tt{3x + 2x + a = 180 \degree} \\ \\ \tt{ \implies \:3x + 2x + 30 \degree \: = 180 \degree} \\ \\ \tt{ \implies \: 5x = 180 \degree - 30 \degree} \\ \\ \tt{ \implies \: 5x = 150 \degree} \\ \\ \tt{ \implies \: x = \frac{150 \degree}{5}} \\ \\ \: \: \: \: \: \: \: \: \: \tt{ \therefore \: \: \underline{\red{ \: \: \: \: x = 30 \degree} \: \: }}$

$\mathfrak{Hence, } \\ \\ \tt{ : \leadsto \: \: 3x = 3 \times \red{30} \degree = 90 \degree} \\ \\ \tt{ : \leadsto \: \: 2x = 2 \times \red{30} \degree = 60 \degree}$

Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathcal{ \purple{ \: \: SOLUTION\: \: } \mid}}}}}$

$\underline{ \bf{ \: \: Given, \: \: }} \\ \\ \: \: \: \: \: \: \huge{ \text{a = 30 \degree}} \\ \\ \underline{ \bf{ \: \: To \: \: find : \: }} \\ \\ \huge{ \text{The value of x = ? \: }}$

$\underline{ \bf{ \: \: We \: \: know \: \: that, \: \: }} \\ \\ \green{ \text{</p><p>The sum of the three angles of a triangle}} \\ \green{ \text{ is equal to 180 \degree}.}$

$\bf{So,} \\ \: \: \: \: \: \: \underline{ \text{ \: In the diagram, \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \sf{3x + 2x + a = 180 \degree} \\ \\ \sf{ \rightarrow \:3x + 2x + 30 \degree \: = 180 \degree} \\ \\ \sf{ \rightarrow \: 5x = 180 \degree - 30 \degree} \\ \\ \sf{ \rightarrow\: 5x = 150 \degree} \\ \\ \sf{ \rightarrow \: x = \frac{150 \degree}{5}} \\ \\ \: \: \: \: \: \: \: \: \: \sf{ \therefore \: \: \underline{\pink{ \: \: \: \: x = 30 \degree} \: \: }}$