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°

6, 10

9, -13

12, -21

18, -23

step-by-step explanation:

you just add 6 to the x-coordinate and subtract 10 from the y-coordinate.

each side has a different length.  

step-by-step explanation: