Smallest angle is [tex]50[/tex]°
Step-by-step explanation:
Here we have , Quadrilateral WXYZ has interior angles that meet the following criteria:
Angles W and X are congruent.
According to question , angles are congruent i.e. Both angle measure same
⇒ [tex]X=W[/tex]
Now ,
• The smallest angle's measure is 100° less than twice the measure of W.
According to above statement we have ,
Smallest angle = [tex]2W-100[/tex]
• The largest angle's measure is 10º more than twice the measure of X. ( correction , in question given as 2X )
According to above statement we have ,
Largest angle = [tex]10+2X=10+2X[/tex]
Now , We know that sum of all 4 angles in 360 i.e.
⇒ [tex]X+W+10+2X+2W-100=360[/tex] { X=W }
⇒ [tex]6W-90=360[/tex]
⇒ [tex]6W=450[/tex]
⇒ [tex]W=75[/tex]
Smallest angle is : [tex]2W-100 = 2(75)-100=50[/tex]
Therefore , Smallest angle is [tex]50[/tex]° .