Question

Find the angle of a triangle if angles are (5x) ,(2x+10) and (3z-10)
(Hint. Sum of the three angles of a triangle is 180°.]​

Answer 1

Correct Question :

Find all the angles of a triangle ,if the angles are (5x) ,(2x+10) and (3x - 10).

Given :

• $\bf{\angle_{1}}$ = 5x

• $\bf{\angle_{2}}$ = (2x + 10)

• $\bf{\angle_{3}}$ = (3z - 10)

To find :

The angles of the triangle.

Solution :

We know that sum of three angles of s triangle sum up to 180°.

So , if we add the given angles in terms x, we can find the value of x and then by substituting the value of x in the angles (in terms of x) , we can find the required value !!

According to the Question , the sum of $\bf{\angle_{1}}$ , $\bf{\angle_{2}}$ , $\bf{\angle_{3}}$ is 180° , so the Equation formed is :

$\underline{\boxed{:\implies \bf{\angle_{1} + \angle_{2} + \angle_{3} = 180^{\circ}}}}$

Now , by substituting the value of angles (in terms of x) , we get :-

$:\implies \bf{5x + (2x + 10) + (3x - 10) = 180^{\circ}}$

$:\implies \bf{5x + 2x + 10 + 3x - 10 = 180^{\circ}}$

$:\implies \bf{10x + 10 - 10 = 180^{\circ}}$

$:\implies \bf{10x = 180^{\circ}}$

$:\implies \bf{x = \dfrac{180^{\circ}}{10}}$

$:\implies \bf{x = 18^{\circ}}$

$\underline{\therefore \bf{x = 18^{\circ}}}$

Hence, the value of x is 18° .

Now putting the value of x in the given angles in terms of x , we get :-

• $\bf{\angle_{1} = 5x}$

$:\implies \bf{\angle_{1} = 5 \times 18^{\circ}}$

$:\implies \bf{\angle_{1} = 90^{\circ}}$

Hence, $\bf{\angle_{1}}$ is 90°.

⠀⠀⠀⠀⠀⠀⠀⠀⠀

• $\bf{\angle_{2} = (2x + 10)}$

$:\implies \bf{\angle_{2} = (2 \times 18^{\circ} + 10)}$

$:\implies \bf{\angle_{2} = (36^{\circ} + 10)}$

$:\implies \bf{\angle_{2} = 46^{\circ}}$

Hence, $\bf{\angle_{2}}$ is 46°.⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• $\bf{\angle_{3} = (3x - 10)}$

$:\implies \bf{\angle_{3} = (3 \times 18^{\circ} - 10)}$

$:\implies \bf{\angle_{3} = (54^{\circ} - 10)}$

$:\implies \bf{\angle_{3} = 44^{\circ}}$

Hence, $\bf{\angle_{3}}$ is 44°.

Thus , the three angles are 90° , 46° and 44°.

Answer 2

$Correct Question :</p><p></p><p>Find all the angles of a triangle ,if the angles are (5x) ,(2x+10) and (3x - 10).</p><p></p><p>Given :</p><p></p><p>\bf{\angle_{1}}∠1 = 5x</p><p></p><p>\bf{\angle_{2}}∠2 = (2x + 10)</p><p></p><p>\bf{\angle_{3}}∠3 = (3z - 10)</p><p></p><p>To find :</p><p></p><p>The angles of the triangle.</p><p></p><p>Solution :</p><p></p><p>We know that sum of three angles of s triangle sum up to 180°.</p><p>So , if we add the given angles in terms x, we can find the value of x and then by substituting the value of x in the angles (in terms of x) , we can find the required value !!</p><p>According to the Question , the sum of \bf{\angle_{1}}∠1 , \bf{\angle_{2}}∠2 , \bf{\angle_{3}}∠3 is 180° , so the Equation formed is :</p><p>\underline{\boxed{:\implies \bf{\angle_{1} + \angle_{2} + \angle_{3} = 180^{\circ}}}}:⟹∠1+∠2+∠3=180∘</p><p>Now , by substituting the value of angles (in terms of x) , we get :-</p><p>\begin{gathered}:\implies \bf{5x + (2x + 10) + (3x - 10) = 180^{\circ}} \\ \\ \\ \end{gathered}:⟹5x+(2x+10)+(3x−10)=180∘</p><p>\begin{gathered}:\implies \bf{5x + 2x + 10 + 3x - 10 = 180^{\circ}} \\ \\ \\ \end{gathered}:⟹5x+2x+10+3x−10=180∘</p><p>\begin{gathered}:\implies \bf{10x + 10 - 10 = 180^{\circ}} \\ \\ \\ \end{gathered}:⟹10x+10−10=180∘</p><p>\begin{gathered}:\implies \bf{10x = 180^{\circ}} \\ \\ \\ \end{gathered}:⟹10x=180∘</p><p>\begin{gathered}:\implies \bf{x = \dfrac{180^{\circ}}{10}} \\ \\ \\ \end{gathered}:⟹x=10180∘</p><p>\begin{gathered}:\implies \bf{x = 18^{\circ}} \\ \\ \\ \end{gathered}:⟹x=18∘</p><p>\begin{gathered}\underline{\therefore \bf{x = 18^{\circ}}} \\ \\ \\ \end{gathered}∴x=18∘</p><p>Hence, the value of x is 18° .</p><p>Now putting the value of x in the given angles in terms of x , we get :-</p><p></p><p>\begin{gathered}\bf{\angle_{1} = 5x} \\ \\ \end{gathered}∠1=5x</p><p></p><p>\begin{gathered}:\implies \bf{\angle_{1} = 5 \times 18^{\circ}} \\ \\ \end{gathered}:⟹∠1=5×18∘</p><p>\begin{gathered}:\implies \bf{\angle_{1} = 90^{\circ}} \\ \\ \end{gathered}:⟹∠1=90∘</p><p>Hence, \bf{\angle_{1}}∠1 is 90°.</p><p>⠀⠀⠀⠀⠀⠀⠀⠀⠀</p><p></p><p>\begin{gathered}\bf{\angle_{2} = (2x + 10)} \\ \\ \end{gathered}∠2=(2x+10)</p><p></p><p>\begin{gathered}:\implies \bf{\angle_{2} = (2 \times 18^{\circ} + 10)} \\ \\ \\ \end{gathered}:⟹∠2=(2×18∘+10)</p><p>\begin{gathered}:\implies \bf{\angle_{2} = (36^{\circ} + 10)} \\ \\ \\ \end{gathered}:⟹∠2=(36∘+10)</p><p>\begin{gathered}:\implies \bf{\angle_{2} = 46^{\circ}} \\ \\ \\ \end{gathered}:⟹∠2=46∘</p><p>Hence, \bf{\angle_{2}}∠2 is 46°.⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀</p><p></p><p>\begin{gathered}\bf{\angle_{3} = (3x - 10)} \\ \\ \\ \end{gathered}∠</p><p></p><p>$