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Scilla [17]
3 years ago
10

Quadrilateral WXYZ has interior angles that meet the following criteria: Angles W and X are congruent . The smallest angle's mea

sure is 100° less than twice the measure of angle W . The largest angle's measure is 10more than twice the measure of angle X Find the measure of the smallest angle in the quadrilateral .
Mathematics
1 answer:
Reptile [31]3 years ago
4 0

Smallest angle is 50°

<u>Step-by-step explanation:</u>

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° .

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