Question

Angles of Similar Triangles Practice
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Question
△GHI∼△LKJ
, and m∠G=30°
, m∠H=80°
, and m∠I=70°
. What are the measures of angles J
, K
, and L
? (2 points)
m∠J =

°
, m∠K =

°
, and m∠L =

Answer 1

In similar triangles, corresponding angles are equal. Since \( \triangle GHI \sim \triangle LJK \), we can use the information from \( \triangle GHI \) to find the angles of \( \triangle LJK \).

Given:
- \( m\angle G = 30^\circ \)
- \( m\angle H = 80^\circ \)
- \( m\angle I = 70^\circ \)

Since the angles in a triangle add up to \( 180^\circ \), let's confirm:

\[
m\angle G + m\angle H + m\angle I = 30^\circ + 80^\circ + 70^\circ = 180^\circ
\]

Now, we can find the measures of angles \( J \), \( K \), and \( L \):

1. \( m\angle J \) corresponds to \( m\angle G \):
\[
m\angle J = m\angle G = 30^\circ
\]

2. \( m\angle K \) corresponds to \( m\angle H \):
\[
m\angle K = m\angle H = 80^\circ
\]

3. \( m\angle L \) corresponds to \( m\angle I \):
\[
m\angle L = m\angle I = 70^\circ
\]

Therefore, the measures of the angles are:
- \( m\angle J = 30^\circ \)
- \( m\angle K = 80^\circ \)
- \( m\angle L = 70^\circ \)

Final answers:
- \( m\angle J = 30^\circ \)
- \( m\angle K = 80^\circ \)
- \( m\angle L = 70^\circ \)