Question

Give the answer of the 3 question ​

Answer 1

Given :

• Three angles of triangle are (x+10°) , (2x+30°) and x° .

To Find :

• Value of x .

Solution :

As we know that Sum of all angles of a triangle is 180° . So ,

$\longmapsto\tt{x+10^{\circ}+2x-30^{\circ}+x^{\circ}=180^{\circ}}$

$\longmapsto\tt{4x^{\circ}+10^{\circ}-30^{\circ}=180^{\circ}}$

$\longmapsto\tt{4x^{\circ}-20^{\circ}=180^{\circ}}$

$\longmapsto\tt{4x^{\circ}=180^{\circ}+20^{\circ}}$

$\longmapsto\tt{4x^{\circ}=200}$

$\longmapsto\tt{x=\cancel\dfrac{200}{4}}$

$\longmapsto\tt\bf{x=50^{\circ}}$

Value of x is 50° ..

_______________________

VERIFICATION :

$\longmapsto\tt{x+10^{\circ}+2x-30^{\circ}+x=180^{\circ}}$

$\longmapsto\tt{50^{\circ}+10^{\circ}+2(50)-30^{\circ}+50^{\circ}=180^{\circ}}$

$\longmapsto\tt{60^{\circ}+100^{\circ}-30^{\circ}+50^{\circ}=180^{\circ}}$

$\longmapsto\tt{160^{\circ}+50^{\circ}-30^{\circ}=180^{\circ}}$

$\longmapsto\tt{210^{\circ}-30^{\circ}=180^{\circ}}$

$\longmapsto\tt\bf{180^{\circ}=180^{\circ}}$

HENCE VERIFIED

Answer 2

$\huge{\underline{\boxed{\bf{Given}}}}$

• 1st angle = x + 10°
• 2nd angle = 2x - 30°
• 3rd angle = x°

$\huge{\underline{\boxed{\bf{Find}}}}$

• What will be the value of x

$\huge{\underline{\boxed{\bf{Diagram}}}}$

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B } \put(1.4,0.3){ \bf {x}^{\circ} }\put(2.7,2.4){ \bf {x+10}^{\circ} } \put(3.2,0.2){ \bf {2x-30}^{\circ} } \end{picture}$

$\huge{\underline{\boxed{\bf{Solution}}}}$

we, know that

$\underbrace{\underline{\boxed{\sf \angle A + \angle B + \angle C = {180}^{ \circ}}}}$

where,

• $\angle$ A = x + 10°
• $\angle$ B = 2x - 30°
• $\angle$ C = x°

So,

$\dashrightarrow\sf \angle A + \angle B + \angle C = {180}^{ \circ}$

$\dashrightarrow\sf x + 10 + 2x - 30 + x = {180}^{ \circ}$

$\dashrightarrow\sf x + 2x + x - 20= {180}^{ \circ}$

$\dashrightarrow\sf 4x - 20= {180}^{ \circ}$

$\dashrightarrow\sf 4x= 180 + 20$

$\dashrightarrow\sf 4x=200$

$\dashrightarrow\sf x= \dfrac{200}{4}$

$\dashrightarrow\sf x={50}^{\circ}$

$\qquad\quad$_____________

Hence, x = 50°