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Problem : Show that the interior angles of a triangle always sum to 180 degrees.

This conclusion is based on the congruence of alternate interior angles when a transversal intersects parallel lines.
The line through A parallel to segment BC is drawn, and according to the congruence of alternate interior angles, the three interior angles of a triangle span half the plane, which is equal to 180 degrees.

Problem : How many triangles must be combined to compose a hexagon?

Four

Problem : Can a triangle have more than one obtuse angle?

No. If it did, then its angle sum would exceed 180 degrees.
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