Question

One angle if a triangle measures 25 and other 2 angles are in a ratio of 14:17 what are the measures of those two angles?

Answer 1

85° and 70°

Step-by-step explanation:

hypothetically if angle A = 25°, and the ratio of the two other angles (B and C) are 14:17, hence;

`(b)/(c) = (14)/(17) \\ 17b = 14c \\ b = (14)/(17) c`

sum of all angles in a triangle equals 180°, therefore:

`a + b + c = 180 \\ 25 + b + c = 180 \\ b + c = 155`

hence, there are two equations:

`b = (14)/(17)c \\ b + c = 155`

replace angle B in the second equation with the first equation:

`( (14)/(17)c) + c = 155 \\ (31)/(17)c = 155 \\ c = 85`

if C = 85°, then to find B:

`b + c = 155 \\ b + 85 = 155 \\ b = 70`

therefore the two other angles are 85° and 70°