Question

if one of the angle of a triangle is 65 and the other two angle are in the ratio of 2:3 find the other angle of solution​

Answer 1

• Other angles of triangle are 46° and 69° respectively.

Step-by-step explanation:

Given:-

• One angle of triangle is 65°.
• Other two angles are in ratio of 2:3.

To find:-

• Other angle.

Solution:-

Let, Other two angles of triangle be '2x' and '3x'.

We know that,

Sum of all interior angles of triangle is equal to 180°.

So,

➝ 2x + 3x + 65° = 180°

➝ 5x + 65° = 180°

➝ 5x = 180° - 65°

➝ 5x = 115°

➝ x = 115°/5

➝ x = 23°

Verification:-

➝ 2x + 3x + 65° = 180°

➝ 5x + 65° = 180°

• Put x = 23°

➝ (5×23)° + 65° = 180°

➝ 115° + 65° = 180°

➝ 180° = 180°

Hence, Verified.

2x = 2×23 = 46°

3x = 3×23 = 69°

Therefore,

Other angles of triangle are 46° and 69° respectively.

Answer 2

$\huge\bold{\mathtt{Question⇒}}$

If one of the angle of a triangle is 65 and the other two angle are in the ratio of 2:3, find the other angles of the triangle.

$\huge\bold{\mathtt{Given⇒}}$

• One of the angle of a triangle is 65.

• The other two angle are in the ratio of 2:3.

$\huge\bold{\mathtt{To\:find⇒}}$

The other two angles.

$\huge\bold{\mathtt{Solution⇒}}$

Let the other two angles are 2x° and 3x° respectively.

We know that:

Sum of all angles of a triangle is 180°.

According to condition,

2x + 3x + 65 = 180

➳ 5x + 65 = 180

➳ 5x = 180 - 65

➳ 5x = 115

➳ x = 115 ÷ 5

➳ x = 23

$\huge\bold{\mathtt{Hence⇒}}$

x = 23

Substitute x with 23.

2x° = (2 × 23)° = 46°

3x° = (3 × 23)° = 69°

$\huge\bold{\mathtt{Therefore⇒}}$

The other two angle are 46° and 69° respectively.

$\huge\bold{\mathtt{Not\:sure\:??}}$

$\huge\bold{\mathtt{Verification⇒}}$

2x + 3x + 65 = 180

Putting the values of the angles.

➳ 46 + 69 + 65 = 180

➳ 180 = 180

So, L.H.S = R.H.S.

Hence, verified.

$\huge\bold{\mathtt{Done}}$

$\large\bold{\mathtt{Hope\:this\:helps\:you.}}$

$\large\bold{\mathtt{Have\:a\:nice\:day.}}$