Quadrilateral WXYZ has interior angles that meet the following criteria:
Angles W and X are congruent.
• The smallest angle's measure is 100° less than twice the measure of W.
• The largest angle's measure is 10º more than twice the measure of 2X.
Find the measure of the smallest angle in the quadrilateral.

Respuesta :

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]° .

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