Question

two triangles are shown in the figure.
are the triangles similar, and why?
○ yes. the triangles are both scalene.
○ yes. the obtuse angles for both triangles are equal.
○ no. the lengths of the sides are not given.
○ no. the corresponding angles are not congruent.

Explanation:

Step1: Find third angle of first triangle

Sum of angles in triangle is $180^\circ$.
Third angle $= 180^\circ - 135^\circ - 15^\circ = 30^\circ$

Step2: Find third angle of second triangle

Sum of angles in triangle is $180^\circ$.
Third angle $= 180^\circ - 135^\circ - 25^\circ = 20^\circ$

Step3: Compare corresponding angles

First triangle angles: $135^\circ, 15^\circ, 30^\circ$
Second triangle angles: $135^\circ, 25^\circ, 20^\circ$
Corresponding angles are not all congruent.

Answer:

No. The corresponding angles are not congruent.