Question

Two angles of a traingle are in the ratio 2:3 and its third angle is 70° find the other two angles of traingle​

Answer 1

Answer :

• The other two angles of triangle are 44⁰ and 66⁰.

Given :

• Two angles of a triangle are in the ratio 2:3
• Third angle is 70⁰

To find :

• Other two angles of a triangle

Solution :

Two angles of a triangle are in the ratio 2 : 3 so,

• Let the ratio be 2x and 3x

Third angle is 70⁰

As we know that

• Sum of all angles in a triangle is equal to 180⁰

According to question,

》2x + 3x + 70⁰ = 180⁰

》5x + 70⁰ = 180⁰

》5x = 180⁰ - 70⁰

》5x = 110⁰

》x = 110⁰/5

》x = 22⁰

Now , we have to find the other two angles of a triangle :

• 2x = 2(22) = 44⁰
• 3x = 3(22) = 66⁰

Hence , The other two angles of triangle are 44⁰ and 66⁰.

Verification :

• First angle = 44⁰
• Second angle = 66⁰
• Third angle = 70⁰

We know that,

• Sum of all angles in a triangle is equal to 180⁰

》44⁰ + 66⁰ + 70⁰ = 180⁰

》180⁰ = 180⁰

Hence , Verified.

Answer 2

Given:-

• Two angles of a traingle are in the ratio 2:3 and its third angle is 70°.

To Find:-

• Other two angles of traingle.

Property Used:-

• Angle Sum Property of Triangle

Solution:-

Let the other two angle be 2x and 3x.

By Angle Sum Property,

Sum of all Angles of Triangle = 180°

$\sf :\implies\:∠1 + ∠2 + ∠3 = 180°$

Here,

• ∠1 = 2x

• ∠2 = 3x

• ∠3 = 70°

Putting values,

$\sf :\implies\:2x+3x+70° = 180°$

$\sf :\implies\:5x= 180°-70°$

$\sf :\implies\:5x=110°$

$\sf :\implies\:x=\dfrac{110}{5}$

$\bf :\implies\:x=22$

• ∠ 1 = 2x = 2 × 22 = 44°

• ∠ 2 = 3x = 3 × 22 = 66°

Hence, The other two angles of the triangle are 44° and 66°.

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