Answer:
[tex]\angle UTS = 40[/tex]
Step-by-step explanation:
Given
See attachment
Required
Find [tex]\angle UTS[/tex]
From the attachment:
[tex]\angle RSU = 70[/tex]
Because it is a rhombus (all equal sides), then the following relationship exists between the angles
[tex]\angle RSU = \angle SUR = 70[/tex]
Considering triangle RSU.
[tex]\angle RSU + \angle SUR + \angle URS = 180[/tex]
This gives:
[tex]70 + 70 + \angle URS = 180[/tex]
[tex]140 + \angle URS = 180[/tex]
[tex]\angle URS = 180-140[/tex]
[tex]\angle URS = 40[/tex]
[tex]\angle UTS = \angle URS = 40[/tex] --- Opposite angle of a rhombus
