Answer:
Problem 1
From smallest to largest:
∠y , ∠w, ∠x
Problem 2
m∠I = 39°
Sides from shortest to longest
GH, HI, GI
Explanation:
For question 1
The ratios of the sides of a triangle to the sine of the angle opposite them is the same
That means the ratios of the sides to each other is the same as the ratio of the sines of the angles opposite them
Since the sine of an angle increases with increasing angle value, the longest side will opposite the greatest angle measurement and the smallest length will be opposite the smallest angle measurement
So in order from smallest to largest
m∠y < m∠w < m∠x
For question 2
Since three angles of a triangle add up to 180°
Missing angle = 180 - (83 + 58)
= 180 - 141
= 39°
From shortest to longest it would be
Side GH < side HI < side GI