Question

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

Answer 1

Answer:

least to greatest: ∠I < ∠J < ∠H

Explanation:

angle I:

cosI = $\frac{10^2+12^2-8^2}{2*10*12}$

I = $cos^{-1} (\frac{3}{4} )$

I = 41.41°

angle H:

cosH = $\frac{10^2+8^2-12^2}{2*10*8}$

H = $cos^{-1} (\frac{1}{8} )$

H = 82.82°

angle J:

cosJ = $\frac{8^2+12^2-10^2}{2*8*12}$

J = $cos^{-1}(\frac{9}{16} )$

J = 55.77°

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

Answer 2

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