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]° .
The measure of the smallest angle in the quadrilateral WXYZ is 50°.
Given to us
In Quadrilateral WXYZ, Angles W and X are congruent .
The smallest angle's measure is 100° less than twice the measure of angle W.
The largest angle's measure is 10more than twice the measure of angle X.
Let the largest angle be represented by 'L' while the smallest angle is represented by 's'.
We know that it is stated in the problem, the largest angle's measure is 10more than twice the measure of angle X.
L = 10° + 2(∠X)
We know that it is stated in the problem, the smallest angle's measure is 100° less than twice the measure of angle W.
s = 2(∠W) -100°
We know the sum of all the angles of a quadrilateral is equal to 360°. therefore,
L + s + ∠W + ∠X = 360°
10° + 2(∠X ) + 2(∠W) - 100° + ∠W + ∠X = 360°
3(∠X ) + 3(∠W) = 360° + 100° - 10°
6(∠X ) = 450° {Congruent angle,∠W = ∠X}
∠X = 75°
∠W = ∠X = 75°
s = 2(∠W) -100°
s = 2(75°) -100°
s = 50°
Hence, the measure of the smallest angle in the quadrilateral WXYZ is 50°.
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