Angles of Similar Triangles Quick Check

Question

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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≅∠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≅∠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≅∠T
, ∠N≅∠R
, ∠O≅∠S

angle upper M congruent to angle upper T , angle upper N congruent to angle upper R , angle upper O congruent to angle upper S
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Answer 1

To find the pairs of congruent corresponding angles in triangles △MNO and △RTS, we need to compare the measures of the angles.

In triangle △MNO:

• m∠M = 78°
• m∠N = 34°
• m∠O = 68°

In triangle △RTS:

• m∠S = 68°
• m∠R = 78°
• m∠T = 34°

Now let's match the angles based on their measures:

• m∠M (78°) corresponds to m∠R (78°), so ∠M ≅ ∠R
• m∠N (34°) corresponds to m∠T (34°), so ∠N ≅ ∠T
• m∠O (68°) corresponds to m∠S (68°), so ∠O ≅ ∠S

Thus, the pairs of congruent corresponding angles are:

• ∠M ≅ ∠R
• ∠N ≅ ∠T
• ∠O ≅ ∠S

The correct response is: ∠M≅∠R, ∠N≅∠T, ∠O≅∠S