Question

Two angles of a triangle are in the ratio (2/3 : 3/2) and the third angle is 50°, then two angles are

​

Answer 1

Here is the answer to your question:

Given: Two angles are in ratio=2/3:3/2

Third angle = 50°

To find : The two angles

Solution: Let in the two angles be 2x/3 and 3x/2

As we know ,

Angle 1 + Angle 2 + Angle 3 =180° (Angle Sum Property of Triangle)

2x/3 + 3x/2 + 50° = 180°

(4x+9x+300°)/6 =180°

13x +300° = 1080°

13x = 780°

x=60°

Therefore The two angles are :

Angle 1 = 2x/3 = 40°

Angle 2= 3x/2 = 90°

Answer 2

→ To Find :

The other two Angles of the triangle .

→ We Know :

$\star$ Sum of three angles of a triangle is 180°.i.e,

$\purple {\sf{\underline{\boxed{\angle_{1} + \angle_{2} + \angle_{3} = 180^{\circ}}}}}$

→ Solution :

Given :

• Ratio of other two angles = $\dfrac{2}{3} : \dfrac{3}{2}$

• Third angle = 50°.

Concept :

Given in the question, the ratio of the two Angles are $\dfrac{2}{3} : \dfrac{3}{2}$ and third side angle is 50°.

Let the two other angles be $\dfrac{2x}{3}$ and $\dfrac{3x}{2}$ , so according to the rule that sum of angles of a triangle is 180°.i.e,

$\purple{\sf{\dfrac{2x}{3} + \dfrac{3x}{2} + 50^{\circ} = 180^{\circ}}}$

So by solving this Equation we will get the value of x .

Calculation :

$\sf{\dfrac{2x}{3} + \dfrac{3x}{2} + 50^{\circ} = 180^{\circ}}$

By solving it, we get :

$\sf{\Rightarrow \dfrac{4x + 9x}{6} + 50^{\circ} = 180^{\circ}}$

$\sf{\Rightarrow \dfrac{13x}{6} + 50^{\circ} = 180^{\circ}}$

$\sf{\Rightarrow \dfrac{13x + 300^{\circ}}{6} = 180^{\circ}}$

$\sf{\Rightarrow 13x + 300^{\circ} = 1080^{\circ}}$

$\sf{\Rightarrow 13x = 300^{\circ} - 1080^{\circ}}$

$\sf{\Rightarrow 13x = 780^{\circ}}$

$\sf{\Rightarrow x = \cancel{\dfrac{780^{\circ}}{13}}}$

$\sf{\Rightarrow x = 60^{\circ}}$

$\purple{\sf{\therefore x = 60^{\circ}}}$

Hence ,the value of x is 60°.

The Other two angles of the triangle :

• First. angle = $\sf{\dfrac{2x}{3}}$

Putting the value of x in the Equation , we get :

$\sf{\Rightarrow \dfrac{2 \times 60^{\circ}}{3}}$

$\sf{\Rightarrow \cancel{\dfrac{120^{\circ}}{3}}}$

$\sf{\Rightarrow 40^{\circ}}$

Hence ,the first angle is 40°.

• Second angle : $\sf{\dfrac{3x}{2}}$

Putting the value of x in the Equation , we get :

$\sf{\Rightarrow \dfrac{3 \times 60^{\circ}}{2}}$

$\sf{\Rightarrow \cancel{\dfrac{180^{\circ}}{2}}}$

$\sf{\Rightarrow 90^{\circ}}$

Hence ,the second angle is 90°.

Thus , the other two angles of the triangle are 40° and 90°.

Extra information :

• Volume of a Cylinder = πr²h

• Volume of a Cube = a³.

• Area of a Sector = lr/2

• surface area of a Cylinder = 2πr(h + r)