Can a right triangle also be obtuse? No Explanation: See solution.
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According to the Corollary to the Triangle Sum Theorem, the non-right angles of a right triangle are complementary.
m∠ B +m∠ C=90^(∘)
Note that the angles of a triangle are always greater than 0. Moreover, since the measures of B and C in the above example add to 90^(∘), then they are both less than 90.
0 < m∠ B < 90 and 0 < m∠ C < 90
The above means that ∠ B and ∠ C are both acute angles. Therefore, the triangle does not have any obtuse angle and thus it cannot be an obtuse triangle.
