Now that we now the value of x, we can calculate the measures of the angles.
m∠ X = (2x+1)^(∘)
m∠ Y = (2x+9)^(∘)
Substitution
(2( 20)+1)^(∘)
(2( 20)+9)^(∘)
Calculation
41 ^(∘)
49 ^(∘)
Comparing the angle measures, we can see that the smallest angle is ∠ X, followed by ∠ Y and then ∠ Z.
m∠ X < m∠ Y Angle-Side Relationships in Triangles.
Angle-Side Relationships in Triangles
If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.
Now, by this theorem, we will look for the corresponding opposite sides.
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Angle & Opposite Side [0.5em]
∠ X & YZ [0.5em]
∠ Y & XZ [0.5em]
∠ Z & XY
From here, we can list the sides in order from smallest to largest.
YZ < XZ < XY
