Question

the angle A of a triangle ABC is equal to the sum of the other two angles. Also, the ratio of the angle B to the angle C is 4:5 . Find the measure of each angle.

Answer 1

Given that 
angle A of a triangle ABC is equal to the sum of the other two angles. i.e
Angle A= Angle B +Angle C
Also given that ratio of angle B to angle C is 4:5
Let Angle B and Angle C be 4x and 5x.
Angle A= 4x+5x
Angle A=9x.


We know that sum of all angles in a triangle is equal to 180 degrees
i.e 
   Angle A + Angle B + Angle C= 180 degrees
                                   9x+4x+5x= 180 degrees
                                              18x=180 degrees
                                                 x= 180/18
                                                 x=10 degrees
Angle A= 9x 
              = 9*10
              =90 degrees
Angle B= 4x
            = 4*10
            = 40 degrees
Angle C= 5x
             = 5*10
              = 50 degrees

Therefore the angles of triangle ABC are 90degrees, 40 degrees, and 50 degrees

Answer 2

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Step-by-step explanation:

By angle sum property of traingle.

A+B+C =180

(4x + 5x ) + 4x + 5x = 180

18x = 180 ,

x = 180/18 , x = 10

A= 9x =90x

B = 4x = 40x

C = 5x = 50 x

This is your answer

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