An exterior angle of a triangle measures 125° and one of the remote interior angles measures 35°. the triangle must be
acute
obtuse
right

The exterior angle of one is 125°. exterior angle is when one of the sides of a triangle is extended and the adjacent angle of that interior angle of the triangle.
the interior angle + exterior angle together make a straight line.
central angle of a straight line is 180°.
interior angle + 125° = 180°
interior angle = 55°
one of the other angles is 35°
the sum of the interior angles of a triangle is 180°
we already know magnitudes of 2 angles, they are 55° and 35°
the third angle - X is
55° + 35° + X = 180°
X + 90° = 180°
X = 90°
the third angle is a right angle.
triangles with 1 right angle is called a right angled triangle 
triangles with 1 obtuse angle is called an obtuse angled triangle 
triangles with all three angles being acute angles is called an acute angled triangle 

in this instance one of the angles is a right angle 
therefore its a right angle triangle