Question

Find the unknown angle from the following figure (2x-10)+3x

Answer 1

✴ Given :-

Two supplementary angles are :

(2x - 10)

(3x + 20)

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

✴ To Find :-

➬ Find these two unknown angles.

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✴ Solution :-

❒ We know that :

$\orange{✯{\green{\text{ Sum of supplementary angles = 180° }}}}$

$\qquad{━━━━━━━━━━━━━━━}$

❒ Finding the value of x :

${\implies{\qquad{\underline{\sf{(2x - 10) + (3x + 20)}} = 180°}}}$

${\implies{\qquad{\sf{(5x - {\underline{10) = 180°}}}}}}$

${\implies{\qquad{\sf{5x = {\underline{180 + 30°}}}}}}$

${\implies{\qquad{\underline{\sf{5}}{\sf{x = {\underline{210}}}}}}}$

${\implies{\qquad{\sf{x = {\underline{\sf{\dfrac{210}{5} }}}}}}}$

${\implies{\qquad{x = {\underline{\sf{\cancel\dfrac{210}{5} }}}}}}$

$\qquad{\qquad{\large{\red{:\longmapsto{\underline{\overline{\boxed{\green{\sf{ x = 42}}}}}}}}}}$

$\qquad{━━━━━━━━━━━━━━━}$

❒ Angles :

∠1 :

$\qquad{:\longmapsto{\sf{∠1 = (2x - 10) }}}$

$\qquad{:\longmapsto{\sf{∠1 = (2 \ times 42 - 10) }}}$

$\qquad{:\longmapsto{\sf{∠1 = (84 - 10) }}}$

$\qquad{\qquad{\large{\red{:\longmapsto{\blue{\underline{\overline{\sf{ ∠1 = 74° }}}}}}}}}$

∠2 :

$\qquad{:\longmapsto{\sf{∠2 = (3x - 20) }}}$

$\qquad{:\longmapsto{\sf{∠2 = (3 \times 42- 20) }}}$

$\qquad{:\longmapsto{\sf{∠2 = (126 - 20) }}}$

$\qquad{\qquad{\large{\red{:\longmapsto{\blue{\underline{\overline{\sf{ ∠2 = 146° }}}}}}}}}$

$\qquad{━━━━━━━━━━━━━━━}$

❒ Verification :

${\implies{\sf{ (2x - 10) + (3x + 20) = 180°}}}$

${\implies{\sf{ (2 \times 42 - 10) + (3 \times 42 + 20) = 180°}}}$

${\implies{\sf{ (84 - 10) + (126 + 20) = 180°}}}$

${\implies{\sf{ 74° + 106° = 180°}}}$

${\implies{\sf{ 180° = 180°}}}$

$\:\:\:\: {\red{\underline{\sf{ LHS = RHS}}}}$

Hence, Verified.

${\green{\underline{▬▬▬▬▬}}{\pink{\underline{▬▬▬▬▬}}{\orange{\underline{▬▬▬▬▬}}{\purple{\underline{▬▬▬▬▬▬}}}}}}$