Are the two triangles below similar? (my guess is c)
a: no, because there are not two pairs of congruent corresponding angles
b: yes, because there are two pairs of congruent corresponding angles
c: no, because the corresponding sides are not proportional
d: yes, because the corresponding sides are proportional

Both triangles have identical inside angles, so the answer should be::

B: Yes, because there are two pairs of congruent corresponding angles

B: Yes, because there are two pairs of congruent corresponding angles.

Step-by-step explanation:

In ΔTUV

∠T+∠U+∠V=180° [By angle sum property of triangle]

⇒ ∠T= 180°-∠V-∠U

⇒ ∠T= 180°-55°-80°

⇒∠T=180°-135°

⇒∠T=45°

Now, in ΔTUV and ΔXYW

∠T=∠X=45° and ∠V=∠W=55°

⇒ ΔTUV ≈ ΔXYW  [AA- similarity criteria of triangles.]

AA Similarity Postulate tells that two triangles are said to be similar if they have two corresponding angles that are congruent in measure.

12

Step-by-step explanation:

3x + 6 + 48 = 90

3x + 54 = 90

3x = 36

x = 12