Question

one of the angle of a triangle is equal to the sum of the other two angles .if the ratio of other two angle is 4:5 , find the measure of all angles of the triangle

Answer 1

Given that one of the angle of a triangle is equal to the sum of the other two angles




Let other two angles are 4x and 5x


And, Other two angles are 4x and 5x




Discussed one angle = 4x + 5x



Discussed one ( first ) angle = 9x




Now, all three angles of the triangle are 9x , 4x and 5x.





Sum of all angles of any triangle = 180°


9x + 4x + 5x = 180°

18x = 180°

x = 180° / 18

x = 10°





Therefore, angles are :

9x = 9 ( 10° ) = 90°

4x = 4( 10 ) = 40°

5x = 5( 10 ) = 50°


$\:$

Answer 2

Solutions :-


Given :

One of the angle of a triangle is equal to the sum of the other two angles.

The ratio of other two angle is 4:5

Let the angles be 4x and 5x

The sum of this two angles =>
4x + 5x = 9x


Now,
We have
First angle = 4x
Second angle = 5x
Third angle = 9x


We know,

Sum of all angles of a triangle is equal to 180°


A/q


=> 4x + 5x + 9x = 180
=> 18x = 180
=> x = 180/18 = 10



Hence,
First angle = 4x = 4 × 10 = 40°
Second angle = 5x = 5 × 10 = 50°
Third angle = 9x = 9 × 10 = 90°