Now that we know the value of x, we can find the measure of each angle.
Expression
Substitution
Measure
m∠ M = (2x+3)^(∘)
(2( 43)+3)^(∘)
89^(∘)
m∠ P = (x-1)^(∘)
( 43-1)^(∘)
42^(∘)
m∠ Q = (x+6)^(∘)
( 43+6)^(∘)
49^(∘)
Comparing the angle measures, we can see that the smallest angle is ∠ P followed by ∠ Q and ∠ M.
∠ P, ∠ Q, ∠ M
Next, let's consider Theorem 5.10 about 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.
cc
Angle & Opposite Side [0.5em]
∠ P & MQ [0.5em]
∠ Q & PM [0.5em]
∠ M & PQ
From here, we can list the sides in order from smallest to largest.
MQ < PM < PQ
