Question
An illustration shows two non-adjacent angles, with angle J K L measuring 34 degrees and angle G H I measuring x degrees. Ray K L is vertical, and ray H I is horizontal.
If ∠LKJ
and ∠GHI
are complementary angles, what is the angle measure of ∠GHI
?
(1 point)
Responses
124°
124 degrees
66°
66 degrees
56°
56 degrees
146°
If ∠LKJ
and ∠GHI
are complementary angles, what is the angle measure of ∠GHI
?
(1 point)
Responses
124°
124 degrees
66°
66 degrees
56°
56 degrees
146°
Answers
GPT-4o mini
To find the angle measure of ∠GHI given that ∠LKJ and ∠GHI are complementary angles, we first need to understand the relationship defined by complementary angles. Complementary angles are two angles that add up to 90 degrees.
From the information given, we know:
- ∠JKL = 34 degrees (this is actually the same as ∠LKJ since the angles are non-adjacent).
- Let's denote ∠GHI as x.
Since ∠JKL (which is 34 degrees) and ∠GHI (which is x) are complementary, we have:
\[
\angle JK = 34^\circ + x = 90^\circ
\]
To find x, we can rearrange the equation:
\[
x = 90^\circ - 34^\circ
\]
\[
x = 56^\circ
\]
Therefore, the measure of ∠GHI is **56 degrees**. The correct response is:
**56°**
From the information given, we know:
- ∠JKL = 34 degrees (this is actually the same as ∠LKJ since the angles are non-adjacent).
- Let's denote ∠GHI as x.
Since ∠JKL (which is 34 degrees) and ∠GHI (which is x) are complementary, we have:
\[
\angle JK = 34^\circ + x = 90^\circ
\]
To find x, we can rearrange the equation:
\[
x = 90^\circ - 34^\circ
\]
\[
x = 56^\circ
\]
Therefore, the measure of ∠GHI is **56 degrees**. The correct response is:
**56°**