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`°

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`° .