An obtuse ∠GHI

Question

has a measure of 135°
. It contains adjacent angles GHJ
and JHI
. ∠GHJ
has a measure of 112°
. What is the measure of ∠JHI
?(1 point)
Responses

90°
90 degrees

68°
68 degrees

15°
15 degrees

23°

Answer 1

To find the measure of angle ∠JHI, we can use the fact that the sum of the measures of adjacent angles is equal to the measure of the larger angle ∠GHI.

Given:

• ∠GHI = 135°
• ∠GHJ = 112°

We can use the following equation:

$$\angle GHI=\angle GHJ+\angle JHI$$

Substituting the known values:

$$135°=112°+\angle JHI$$

Now, we can solve for ∠JHI:

$$\angle JHI=135°-112°=23°$$

Therefore, the measure of ∠JHI is 23°.

Answer 2

If m∠ABC
is 160°
, and m∠ABD
is 92°
, what is the angle measure of DBC
? ∠ABD
and ∠DBC
are adjacent angles inside ∠ABC
.(1 point)
Responses

80°
80 degrees

160°
160 degrees

68°
68 degrees

92°