Question

Angles of Similar Triangles Quick Check
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Question
In △MNO
, m∠M=78°
, m∠N=34°
, and m∠O=68°
. In △RTS
, m∠S=68°
, m∠R=78°
, and m∠T=34°
. Describe the pairs of congruent corresponding angles in the two triangles.(1 point)
Responses

∠M≅∠R
, ∠N≅∠S
, ∠O≅∠T

angle upper M congruent to angle upper R , angle upper N congruent to angle upper S , angle upper O congruent to angle upper T

∠M≅∠R
, ∠N≅∠T
, ∠O≅∠S

angle upper M congruent to angle upper R , angle upper N congruent to angle upper T , angle upper O congruent to angle upper S

∠M≅∠S
, ∠N≅∠T
, ∠O≅∠R

angle upper M congruent to angle upper S , angle upper N congruent to angle upper T , angle upper O congruent to angle upper R

∠M≅∠T
, ∠N≅∠R
, ∠O≅∠S

Answer 1

To determine the pairs of corresponding angles in the triangles \( \triangle MNO \) and \( \triangle RTS \), we can align their angles based on their measures:

- In \( \triangle MNO \):
- \( m\angle M = 78^\circ \)
- \( m\angle N = 34^\circ \)
- \( m\angle O = 68^\circ \)

- In \( \triangle RTS \):
- \( m\angle R = 78^\circ \)
- \( m\angle S = 68^\circ \)
- \( m\angle T = 34^\circ \)

Now, we can match the angles:

- \( m\angle M = 78^\circ \) corresponds to \( m\angle R = 78^\circ \) → \( \angle M \cong \angle R \)
- \( m\angle N = 34^\circ \) corresponds to \( m\angle T = 34^\circ \) → \( \angle N \cong \angle T \)
- \( m\angle O = 68^\circ \) corresponds to \( m\angle S = 68^\circ \) → \( \angle O \cong \angle S \)

Thus, the corresponding angles are:

- \( \angle M \cong \angle R \)
- \( \angle N \cong \angle T \)
- \( \angle O \cong \angle S \)

So, the correct response is:

**∠M≅∠R, ∠N≅∠T, ∠O≅∠S**