Question

ΔMNO has m∠M=63 degrees and m∠O=71 degrees. ΔRST has m∠R=58 degrees and m∠T=71 degrees. Applying the proof of the AA Similarity Theorem, is △MNO∼△RST ?(1 point)
Responses

Yes, m∠N≅m∠S=51 degrees.
Yes, m∠N≅m∠S=51 degrees.

No, they are not similar. MN≠RS .
No, they are not similar. MN≠RS .

Yes, m∠N≅m∠S=46 degrees.
Yes, m∠N≅m∠S=46 degrees.

No, they are not similar. m∠N=46 degrees and m∠S=51 degrees

Answer 1

To determine if triangles ΔMNO and ΔRST are similar using the AA (Angle-Angle) Similarity Theorem, we can follow these steps:

1. **Find m∠N in ΔMNO**:
- The sum of angles in a triangle is 180 degrees. In ΔMNO:
\[
m∠N = 180° - m∠M - m∠O
\]
\[
m∠N = 180° - 63° - 71° = 46°.
\]

2. **Find m∠S in ΔRST**:
- Similarly, for triangle ΔRST:
\[
m∠S = 180° - m∠R - m∠T
\]
\[
m∠S = 180° - 58° - 71° = 51°.
\]

3. **Compare the angles**:
- In ΔMNO, we have:
- m∠M = 63°
- m∠O = 71°
- m∠N = 46°
- In ΔRST, we have:
- m∠R = 58°
- m∠T = 71°
- m∠S = 51°

Now, we check the corresponding angles:
- m∠M (63°) is not equal to m∠R (58°).
- m∠O (71°) is equal to m∠T (71°).
- m∠N (46°) is not equal to m∠S (51°).

Since not all pairs of corresponding angles are equal, ΔMNO is **not similar** to ΔRST.

The correct response is:
**No, they are not similar. m∠N=46 degrees and m∠S=51 degrees.**