Answer:
The measure of the smallest angle is 50 degrees
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