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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

146°
146 degrees

56°
56 degrees
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Answer 1

To find the measure of angle \( GHI \), we use the fact that complementary angles add up to \( 90^\circ \). Given that \( \angle JKL = 34^\circ \) and \( \angle GHI \) is complementary to \( \angle JKL \), we set up the following equation:

\[ \angle JKL + \angle GHI = 90^\circ \]

Substituting the given value for \( \angle JKL \):

\[ 34^\circ + \angle GHI = 90^\circ \]

To solve for \( \angle GHI \), we subtract \( 34^\circ \) from \( 90^\circ \):

\[ \angle GHI = 90^\circ - 34^\circ = 56^\circ \]

Therefore, the measure of \( \angle GHI \) is \( 56^\circ \).

The correct response is:

56°