Answer:
see explanation
Step-by-step explanation:
The opposite angles of a rhombus are congruent
∠T = ∠R = 120° ( opposite angles )
The triangle RSU is isosceles since the sides of the rhombus are congruent
Thus the base angles ∠RUS and ∠RSU are equal
The sum of the 3 angles in a triangle = 180°, hence
base angles = 180° - 120° = 60°
hence ∠RSU = [tex]\frac{60}{2}[/tex] = 30°
Answer:
1. 120°
2. 30°
Step-by-step explanation:
Consider rhombus RSTU. In each rhombus two opposite angles are always congruent, then
m∠T=m∠R=120°.
The diagonals of the rhombus are rhombus's angles bisectors, then
[tex]m\angle RSU=\dfrac{1}{2}m\angle S.[/tex]
The sum of two consecutive angles in a rhombus is always equal to 180°. Since m∠R = 120°, then
m∠S=180°-m∠R=180°-120°=60°
and
[tex]m\angle RSU=\dfrac{1}{2}\cdot 60^{\circ}=30^{\circ}.[/tex]
