Question

Order the angle measures , , and from least to greatest.

(Note that the figure is not drawn to scale.)

Answer 1

Mark the theorem below

• The angle which measures biggest the opposite side of that angle is biggest.

Here

• 8<10<12
• JH<IH<JI

Now

• <I < <J < <H

Answer 2

least to greatest: ∠I < ∠J < ∠H

Step-by-step explanation:

angle I:

cosI =
`(10^2+12^2-8^2)/(2*10*12)`

I =
`cos^(-1) ((3)/(4) )`

I = 41.41°

angle H:

cosH =
`(10^2+8^2-12^2)/(2*10*8)`

H =
`cos^(-1) ((1)/(8) )`

H = 82.82°

angle J:

cosJ =
`(8^2+12^2-10^2)/(2*8*12)`

J =
`cos^(-1)((9)/(16) )`

J = 55.77°

They sum up to 180°, so the steps are correct.