Answer
From the options, we can see that
Options A and C are the only correct options.
- Triangle JKL and Triangle LMN have only one pair of congruent angles.
- Triangle JKL has angles that measure 50°, 60° and 70°.
Explanation
To pick the right statements, we will solve the triangles, starting at the point L.
The angles that are directly opposite each other here are equal to each other.
(6x - 2)° = (5x + 10)°
6x - 2° = 5x + 10°
6x - 5x = 10° + 2°
x = 12°
Noting that the sum of angles in a triangle is 180°, we can solve for the other angles in the triangles.
For triangle JKL
6x - 2° = 6(12°) - 2° = 72° - 2° = 70°
5x = 5(12°) = 60°
Third angle + 60° + 70° = 180°
Third angle + 130° = 180°
Third angle = 180° - 130°
Third angle = 50°
Therefore, the angles of triangle JKL are 50°, 60° and 70°.
For triangle LMN
5x + 10 = 5(12°) + 10° = 60° + 10° = 70°
6x - 7° = 6(12°) - 7° = 72° - 7° = 65°
Third angle + 70° + 65° = 180°
Third angle + 135° = 180°
Third angle = 180° - 135°
Third angle = 45°
Therefore, the angles of triangle LMN are 45°, 65° and 70°.
For the two triangles to be siilar, all three angles must be the same or congruent.
But we can see that only one angle is common to both triangles.
Hope this Helps!!!
