Answer:
x=27°
y=4 units
Step-by-step explanation:
To find x:
The sum of all the angles in a quadrilateral is 360°. In a rhombus (you know it's a rhombus because it's a quatrilateral where all the sides are congruent), opposite angles are congruent. Because you're given that the measure of ∠T is 127°, you also know that m∠V=127°. You also know that m∠U=m∠S=(2x-1)°.
Using this information, set up an equation.
127+127+(2x-1)+(2x-1)=360
You can just divide both sides by 2 to get:
127+(2x-1)=180
Then, just solve for x.
127+2x-1=180
2x+126=180
2x=54
x=27°
To find y:
All the sides are given to be congruent. That's what the little marks on the sides mean, and that's how we knew it was a rhombus earlier.
So SV=VU=UT=TS
SV=6y-5
VU=3y+7
Since SV=VU:
6y-5=3y+7
Solve for y.
3y=12
y=4
Hope I could help!
