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Answer:
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°