Question

15. One of the angles of a triangle is equal to the sum of the other two angles. If the ratio of the other two angles
is 4:5, find the angles of the triangle,
​

Answer 1

Step-by-step explanation:

Let a, b, c be the angles of the triangle.

As you know, a+b+c=180° (1) in a triangle.

a=b+c (2)

b/c = 4/5, so 5b=4c or c=5/4 b (3)

From (2) & (3): a=b + 5/4 b = 9/4 b or a = 9/4 b (4)

From (1)&(3)&(4) one gets:

9/4 b + b + 5/4 b = 180°

It means that 18/4 b = 180° so,

b = 40°. Then c = 5/4 • 40° and

c = 50° .

a = b + c = 40° + 50° = 90°

Your angles are 90° , 50° and 40°.