Question

Find the value of x in the given figure.​

Answer 1

Answer:

(2x+60°)+(3x-40°)=180°

5x+20°=180°

5x=180°-20°

5x=160°

x=160/5

x=32(answer)

Answer 2

$\huge\underline \mathfrak\purple{Solution} \: -$$\orange{{\fbox\pink{\tt{sum\:of\:\:linear\:pair = 180°}}}}$

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So here,

$∠ROP + ∠ROQ = 180° \\ \\ \implies(2x + 60)° + (3x - 40)° = 180° \\ \implies2x + 60 + 3x - 40 = 180\\ \implies3x + 2x + 60 - 40 = 180\\ \implies5x + 20 = 180$

• transposing like terms to obtain value of x we get,

$5x + 20 = 180 \\ \implies5x = 180 - 20 \\ \implies5x = 160 \\ \implies x = \frac{160}{5} \\ \boxed{x = 32°}$

∴ value of x is 32°

(*refer to the attachment in the question)

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✍️Something you need to know:

• Two angles having common vertex and a common arm are called adjacent angles. Also, their non-common arms are on different sides of the common arm.

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• Linear pair of angles are adjacent angles whose sum of always equal to 180°

• Here, in the given question ∠ROP & ∠ROQ are forming a pair of linear angles. Hence, we applied the above solution.

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