Question

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

ratio of other two angles is 4:5, find measures of all angles of the triangle​

Answer 1

Answer:

Let the other 2 angles of triangle be 4x and 5x.

The sum of 2 angles of triangle = 1 angle of triangle.

Therefore, 3rd angle = the sum of 2 angles of triangle

3rd angle = 4x + 5x = 9x

Therefore, 9x + 5x + 4x = 180° [sum of all angle of triangle = 180°]

18x = 180°

x = 180°/18

x = 10

Therefore angles = 4x, 5x and 9x.

= 4(10), 5(10), 9(10)

= 40°, 50°, 90°.

Answer 2

Step-by-step explanation:

let the angles be a, b and c

given a = b + c

also given b : c = 4 : 5

therefore b = 4x and c = 5x

now, as a = b + c, a = 4x + 5x => 9x

=> a + b + c = 180° [ angle sum property of ∆ ]

=> 9x + 4x + 5x = 180

=> 18x = 180

=> x = 10

angle b = 4x => 4*10 = 40°

angle c = 5x => 5*10 = 50°

angle a = b + c => 40° + 50° => 90°

all tne three angles are 90°, 50° and 40°