Question

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.

Answer 1

Smallest angle is $50$°

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

⇒ $X=W$

Now ,

• The smallest angle's measure is 100° less than twice the measure of W.

According to above statement we have ,

Smallest angle = $2W-100$

• 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 = $10+2X=10+2X$

Now , We know that sum of all 4 angles in 360 i.e.

⇒ $X+W+10+2X+2W-100=360$      { X=W }

⇒ $6W-90=360$

⇒ $6W=450$

⇒ $W=75$

Smallest angle is :  $2W-100 = 2(75)-100=50$

Therefore , Smallest angle is $50$° .