Question

the angles of a triangle are (x-35⁰), (x-25⁰) and (x/2-10⁰), then find x.​

Answer 1

Given:-

• ∠A = (x - 35)°
• ∠B = (x - 25)°
• ∠C = (x/2 - 10)°

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To find:-

• Value of x.

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Solution:-

We Know that ,

• The sum of the interior angles of a triangle is 180°.

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Here,

• ∠A + ∠B + ∠C = 180°

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According to the question,

→ (x - 35)° + ( x - 25 )° + (x/2 - 10)° = 180°

→ x - 35 + x - 25 + x/2 -10 = 180°

→ 2x + x/2 - 70 = 180°

→ (4x + x )/2 = 180° + 70°

→ 5x/2 = 250°

→ 5x = 250° × 2

→ 5x = 500°

→ x = 100°

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Hence,

• ∠A = ( x - 35 )° = 100 - 35 = 65°
• ∠B = ( x - 25 )° = - 25 = 75°
• ∠C = ( x/2 - 10 )° = 50 - 10 = 40°

Answer 2

Answer:

$\Large \star \: \bf { \pmb{Given:}}$

• $\leadsto\sf\angle \: {A }= (x - 35) \degree$
• $\leadsto \sf\angle \: {B}= (x - 25) \degree$
• $\sf{ \angle{C} = \big( \dfrac{x}{2} - 10 \big) \degree}$

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$\Large \star \: \bf { \pmb{To \: find: }}$

• $\leadsto\sf{Value \: of \: x.}$

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$\Large \star \: \bf { \pmb{Solution:}}$

We Know that ,The sum of the all angles of a triangle is 180°.

$: \implies\bf \pink{\angle \: {A} + \angle \: {B} + \angle \: {C}} = \purple {180 \degree}$

According to the question,

${: \implies \bf \pink{ (x - 35)° + ( x - 25 )° + \big( \dfrac{x}{2} - 10 \big)°} = \purple {180°}}$

${ : \implies \bf \pink{(x + x + \dfrac{x}{2} ) + {\big(}( - 35 \degree) ( - 25 \degree) (+ 10 \degree) \big) }= \purple{ 180 \degree}}$

${ : \implies \bf \pink {\big( \dfrac{(x \times 2) +( x \times 2 )+ (x)}{2} \big) + ( - 75 \degree) } = \purple{ 180 \degree}}$

${ : \implies \bf \pink{ \big(\dfrac{2x + 2x + x}{2} \big) + ( - 75 \degree)}= \purple{180 \degree}}$

$: \implies \bf \pink{\dfrac{5x}{2} + ( - 70 \degree) } = \purple{180 \degree}$

$: \implies \bf \pink{\dfrac{5x}{2}} = \purple{180 \degree + 70 \degree }$

$: \implies \bf \pink{\dfrac{5x}{2}} = \purple{250 \degree }$

$: \implies \bf \pink{x} = \purple {\dfrac{250 \times 2}{5}}$

$: \implies \bf \pink{ x }= \purple {\dfrac{500}{5} }$

$\: \: \: \: \: \: \large \underline{\boxed{\red{\frak {\pmb{x =100 \degree}}}}}$

Therefore.

• ${ \leadsto \sf{ \angle \: A = ( x - 35 ) \degree = 100 - 35 = 65 \degree}}$
• $\leadsto \sf \angle \: B = ( x - 25) \degree = - 25 = 75 \degree$
• ${ \leadsto \sf \angle \: C = ( x/2 - 10 ) \degree = 50 - 10 = 40 \degree}$

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$\Large \star \:\bf{ \pmb{Verification:}}$

${: \implies \bf \pink{ (x - 35)° + ( x - 25 )° + \big( \dfrac{x}{2} - 10 \big)°} = \purple {180°}}$

Substuting the value of x=100⁰.

${: \implies \bf \pink{ (100- 35)° + ( 100 - 25 )° + \big( \dfrac{100}{2} - 10 \big)°} = \purple {180°}}$

${: \implies \bf \pink{ (65)° + (75 )° + \big( \dfrac{100 - 20}{2} \big)°} = \purple {180°}}$

${: \implies \bf \pink{ (65)° + (75 )° + \big( \cancel \dfrac{80}{2} \big)°} = \purple {180°}}$

${: \implies \bf \pink{ (65)° + (75 )° +{(40})°} = \purple {180°}}$

$: \implies\bf \pink{180°} = \purple {180°}$

$\: \: \: \: \: \: \large \underline{\boxed{\bf \red{LHS = RHS}}} \\ \: \: \: \: \: \sf \star \: \underline{Hence \: Verified } \: \star$