Answer:
m∠SWX=39°, and m∠VWY=51°
Step-by-step explanation:
∠XWU and ∠VWY are vertical angles. Vertical angles are congruent.
∠XWU=∠VWY
we are given ∠XWU=(7x+2)° and ∠VWY=(4x+23)°, so:
7x+2=4x+23
3x+2=23
3x=21
x=7
Now substitute x for 7 in both expressions to get the measures of the angles.
∠XWU=(7(7)+2)°=(49+2)°=51°
∠VWY is also 51° because it is congruent to ∠XWU, but just to make sure:
∠VWY=(4(7)+23)°=(28+23)°=51°
we also need ∠SWX. We can see it makes a right angle with ∠XWU, so their sum is 90°.
∠SWX+51=90
∠SWX=39°
