Question

1. choose the correct answer.

a corollary of the triangle sum theorem states that the acute angles of a right triangle are____
adjacent
supplementary
remote
complementary

1. choose the correct answer.

a corollary of the triangle sum theorem states that a triangle can contain no more than one____angle or obtuse angle.
interior
acute
right
straight

Explanation:

• For question 20:
• Recall the Triangle Sum Theorem which states that the sum of the interior angles of a triangle is \(180^{\circ}\). In a right - triangle, one angle is \(90^{\circ}\). Let the two acute angles be \(x\) and \(y\). Then \(x + y+90^{\circ}=180^{\circ}\), so \(x + y = 90^{\circ}\). Complementary angles are two angles whose sum is \(90^{\circ}\).
• For question 21:
• Again, using the Triangle Sum Theorem (\(\angle A+\angle B+\angle C = 180^{\circ}\)). If there were two right angles (\(\angle A=\angle B = 90^{\circ}\)), then \(\angle C=0^{\circ}\), which is not possible for a triangle. Similarly, if there were two obtuse angles (say \(\angle A>90^{\circ}\) and \(\angle B > 90^{\circ}\)), then \(\angle A+\angle B+\angle C>180^{\circ}\). A right angle is \(90^{\circ}\) and an obtuse angle is greater than \(90^{\circ}\).

Answer:

1. complementary
2. right