Let the angles of a right-angled triangle be a, b and c. From the theorem on the sum of the angles of a triangle, it is known that the sum of all the angles of any triangle is 180 degrees:
a + b + c = 180 degrees.
Since, by condition, a right-angled triangle is given, one of its angles is 90 degrees. Let the angle a = 90 degrees.
Let’s denote the angle b as x, then the angle c will be equal to x – 38, since it is 38 degrees less by condition.
90 + x + x – 38 = 180;
2x = 180 – 90 + 38;
2x = 128;
x = 128/2;
x = 64 degrees.
Angle b = x = 64 degrees.
Then the angle c is equal to:
c = x – 38 = 64 – 38 = 26 (degrees).
Answer: angle b = 64 degrees, angle c = 26 degrees.
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