Question

if the interior angles of a triangle are 15, 15(x+y), and 25y and the relation between x and y is given by 5x-4y+2=0, then what is the measure of the smallest angle of the triangle​

Answer 1

The sum of 3 angles inside a triangle is 180 deg, then:

=> 15 + 15(x + y) + 25y = 180

=> 15x + 40y = 165 (1)

And we have:

5x - 4y + 2 = 0

=> 5x - 4y = -2

=> 15x - 12y = -6 (2)

From (1) and (2), we have:

52y = 171

=> y = 171/52

=> 5x - 4 x 171/52 = -2

=> 5x = -2 + 171/13

=> x = 145/65

=> First angle: 15 deg

=> Second angle: 15*(145/65 + 171/13) = 82.788 deg

=> Third angle = 25 x 171/52 = 82.211

=> Minimum angle: 15 deg

Hope this helps!

:)