Answer: 65 degrees
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Explanation:
Let x be the measure of the base angles of the isosceles triangle (indicated by the tickmarks).
The base angles of such an isosceles triangle are congruent.
Use the fact that the interior angles of a triangle add to 180.
x+x+130 = 180
2x+130 = 180
2x = 180-130
2x = 50
x = 50/2
x = 25
Now move your attention to the largest triangle, aka the right triangle.
The lower acute angle is 25, which is what we just found earlier.
The angle w is therefore 90-x = 90-25 = 65
The two acute angles of any right triangle are complementary. They add to 90 degrees.