Question

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

Answer 1

Answer:

Given :-

• The angles of a triangle is (5x)°, (2x + 10)° and (3x - 10)°.

To Find :-

• What are the angles of a triangle.

Solution :-

Let,

➲ First Angle = (5x)°

➲ Second Angle = (2x + 10)°

➲ Third Angle = (3x - 10)°

As we know that :

✪ Sum Of All Angles Of Triangle = 180°

According to the question by using the formula we get,

⇒ (5x)° + (2x + 10)° + (3x - 10)° = 180°

⇒ 5x + 2x + 10° + 3x - 10° = 180°

⇒ 5x + 2x + 3x + 10° - 10° = 180°

⇒ 7x + 3x + 10° - 10° = 180°

⇒ 10x = 180°

⇒ x = 180°/10

⇒ x = 18°/1

➦ x = 18°

Hence, the required angles of a triangle are :

❒ First Angle Of Triangle :

↦ First Angle = 5x

↦ First Angle = 5(18°)

↦ First Angle = 5 × 18°

➠ First Angle = 90°

❒ Second Angle Of Triangle :

↦ Second Angle = 2x + 10

↦ Second Angle = 2(18°) + 10

↦ Second Angle = 2 × 18° + 10

↦ Second Angle = 36° + 10

➠ Second Angle = 46°

❒ Third Angle Of Triangle :

↦ Third Angle = 3x - 10

↦ Third Angle = 3(18°) - 10

↦ Third Angle = 3 × 18° - 10

↦ Third Angle = 54° - 10

➠ Third Angle = 44°

∴ The angles of a triangle is 90°, 46° and 44° respectively.

Answer 2

$\large \bold \: {\underline{ \sf{ \underline{\red{ Given :}}}}}$

$\sf{\angle_{1}= 5x}$

$\sf{\angle_{2}= (2x + 10)}$

$\sf{\angle_{3} = (3z - 10)}$

$\large \bold \: {\underline{ \sf{ \underline{\pink{ To\: Find :}}}}}$

The angles of the triangle.

$\large \bold \: {\underline{ \sf{\blue{ \underline{ Solution :}}}}}$

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°.