In a rhombus, an altitude from a vertex of an obtuse angle bisects to opposite side. Find het measures of the angles of the rhombus.

The angles are : 30° , 90° , 60° and 120°

Step-by-step explanation:

In a rhombus the obtuse angles measure up to 120° while the acute angles measure up to 60°

In other to find the net measure of the angles

we will draw  altitude from the vertex to form a right angled triangle and it will as well bisect the opposite side.

let the base of the right angled triangle ( opposite the obtuse angle ) = 1/2 x

side( hypothenuse ) of rhombus = x

sine = opposite / hypothenuse

hence sine x =  1/2 x / x

∴ sin x = 1/2

therefore to determine the value of x

sin^-1 ( x ) = sin^-1 ( 1/2 )

hence ; x = 30

given that the sum of the angles in a triangle = 180 . hence the third angle ( the acute angle ) = 180 - 90 - 30 = 60°

Given that the acute angle and the obtuse angle of a rhombus is  supplementary

hence the value of the obtuse angle = 180° - 60° =  120°

{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