Question

If the measures of angles of a triangle are(x-35) degree ,(x-25)degree and (1/2x-10)degree .Find the value of x.​

Answer 1

AnswEr :

$\bold{Given}\begin{cases}\sf{Angle_1=(x-35)\degree} \\ \sf{Angle_2=(x-25)\degree}\\ \sf{Angle_3=\bigg(\dfrac{1}{2}x-10\bigg)\degree}\\\sf{Find\:the\:value\:of\:x?}\end{cases}$

• Let's Head to the Question Now :

$\longrightarrow \tt Sum \: of \: Angles \: of \:Triangle = 180\degree \\ \\ \longrightarrow \tt Angle_1 + Angle_2 + Angle_3 = 180 \\ \\ \longrightarrow \tt(x - 35) + (x - 25) + \bigg( \dfrac{1}{2}x - 10 \bigg) = 180\degree \\ \\ \longrightarrow \tt x - 35 + x - 25+ \dfrac{x}{2} - 10 = 180 \\ \\ \longrightarrow \tt \bigg(x + x + \dfrac{x}{2} \bigg) - 35 - 25 - 10 = 180 \\ \\ \longrightarrow \tt \bigg( \dfrac{2x + 2x + x}{2} \bigg) - 70 = 180 \\ \\ \longrightarrow \tt \dfrac{5x }{2} = 180 + 70 \\ \\ \longrightarrow \tt \dfrac{5x}{2} = 250 \\ \\ \longrightarrow \tt x = \cancel{250} \times \dfrac{2}{ \cancel5} \\ \\ \longrightarrow \tt x =50 \times 2 \\ \\ \longrightarrow \boxed{ \red{\tt x =100\degree}}$

⠀

∴ Therefore, Value of x will be 100°.

$\rule{300}{2}$

• V E R I F I C A T I O N :

$\Longrightarrow \tt Sum \: of \: Angles \: of \:Triangle = 180\degree \\ \\ \Longrightarrow \tt Angle_1 + Angle_2 + Angle_3 = 180 \\ \\ \Longrightarrow \tt(x - 35) + (x - 25) + \bigg( \dfrac{1}{2}x - 10 \bigg) = 180\degree \\ \\ \Longrightarrow \tt(100 - 35) + (100 - 25) + \bigg( \cancel\dfrac{100}{2} - 10 \bigg) = 180\degree \\ \\ \Longrightarrow \tt65+75 +(50 - 10) = 180\degree \\ \\ \Longrightarrow \tt140+40 = 180\degree \\ \\ \Longrightarrow \blue{ \tt 180\degree= 180\degree} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\underline\frak{Hence,\: Verified}$

Answer 2

$\bold{\Huge{\underline{\boxed{\sf{\pink{ANSWER\::}}}}}}$

$\bold{\Large{\underline{Given\::}}}}}$

If the measures of angles of a triangle are (x-35)° , (x-25)° & (1/2x- 10)°.

$\bold{\Large{\underline{\sf{\red{To\:find\::}}}}}$

The value of x.

$\bold{\Large{\underline{\sf{\green{Explanation\::}}}}}$

We know that formula of the perimeter of triangle:

→ Side + Side + Side

&

Sum of all sides of triangle= 180°

$\bold{We have,}\begin{cases}\\ \sf{First\:angle\:of\:triangle=(x-35)\degree}\\ \sf{Second\:angle\:of\:triangle=(x-25)\degree}}\\ \sf{Third\:angle\:of\:triangle=(\frac{1}{2} x-10)\degree}\end{cases}$

Therefore,

→ (x-35)° + (x-25)° + $(\frac{1}{2} x-10)°$= 180°

→ x - 35° + x - 25° + 1/2x -10 = 180°

→ x + x + 1/2x - 70° = 180°

→ 2x + 1/2x - 70° = 180°

→ $\bold{\frac{4x+x}{2} -70\degree=180\degree}$

→ $\bold{\frac{5x}{2} =180\degree+70\degree}$

→ $\bold{\frac{5x}{2} =250\degree}$

→ 5x = 250×2

→ 5x = 500

→ x = $\bold{\cancel{\frac{500}{5} }}$

→ x = 100°

Thus,

The value of x is 100°.