Question

2. One of the angle of a triangle is equal to sum
of othet two. Ti the ratio of others two angles is
2:3 find the angle.​

Answer 1

Answer:

36   ,54    ,90  

Step-by-step explanation:

Let one angle of the triangle be ∠A and the other two triangles be ∠B,∠C.  

Given, one of angles of a triangle is equal to the sum of the other two triangles.

⟹∠A=∠B+∠C  

⟹∠A=3x+2x=5x

Sum of 3 angles of the triangle = 180  

=∠A+∠B+∠C  

=5x+3x+2x  

⟹x=18

∴∠A=18×5=90  

.:∠B=3×18=54  

∴∠C=2×18=36  

Answer 2

Given:-

• One of the Angle of a triangle is equal to sum of other two Angles.

• Ratio of others two Angles is 2 : 3.

To Find:-

• The Angles of the Triangle

Property Used:-

• Angle Sum Property of Triangle

Solution:-

According to question,

$\bf :\implies\:∠3=∠1 + ∠2$

As given, The Ratio of other two angles as 2:3.

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

Putting values,

$\bf :\implies\:∠3=2x+ 3x$

$\bf :\implies\:∠3 =5x$

Using Angle Sum Property,

$\bf :\implies\:∠1 + ∠2 + ∠3= 180°$

$\bf :\implies\:2x + 3x + 5x= 180°$

$\bf :\implies\:10x= 180°$

$\bf :\implies\:x= \dfrac{180°}{10}$

$\bf :\implies\:x= 18$

Putting value of x,

• $\bf ∠1 = 2x = 2 \times 18 = 36°$

• $\bf ∠2 = 3x = 3 \times 18 = 54°$

• $\bf ∠3 = 5x = 5 \times 18 = 90°$

Hence, The Angles of the Triangle are 26°, 54° and 90°.

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