Two angles of a quadrilateral measure 40° and 180°. The other two angles are in a ratio of 13:15. What are the measures of those two angles?

Step-by-step explanation:

Two angles are given

1st angle = 40° 2nd angle = 180°

And let other two angels be 13 x and 15x

40° + 180° + 13x + 15x = 360° <Being sum of angles of quadrilateral >

220° + 28x = 360°

28x = 360° - 220°

28x = 140°

x = 140° / 28

Therefore x = 5°

Measures of two angles

13x = 13 * 5° = 65°

15x = 15 * 5° = 75°

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1