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

The measure of the smallest angle is 50 degrees

Step-by-step explanation:

The complete question is

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.

Let

Y ---> the measure of the smallest angle

Z ---> the measure of the largest angle

Remember that the sum of the interior angles in any quadrilateral must be equal to 360 degrees

so

W+X+Y+Z=360º > equation A

Angles W and X are congruent

so

X=W > equation B

substitute equation B in equation A

W+W+Y+Z=360º

2W+Y+Z=360º > equation C

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

so

Y=2W-100 > equation D

The largest angle's measure is 10º more than twice the measure of 2X

Z=2X+10

Remember that X=W

so

Z=2W+10 > equation E

substitute equation D and equation E in equation C

2W+(2W-100)+(2W+10)=360º

solve for W

6W=360º+90º

W=450º/6

W=75º

Find the measure of the smallest angle

Y=2W-100

substitute the value of W

Y=2(75º)-100º=50º

therefore

The measure of the smallest angle is 50 degrees

answer: 140

step-by-step explanation:

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