Question

1.6 practice with calcchat and calcview
in exercises 1 - 4, use the diagrams. (see example 1.)

1. name a pair of adjacent complementary angles.
2. name a pair of adjacent supplementary angles.
3. name a pair of nonadjacent supplementary angles.
4. name a pair of nonadjacent complementary angles.

Explanation:

Step1: Recall angle - pair definitions

Complementary angles add up to 90°, supplementary angles add up to 180°. Adjacent angles share a common side and a common vertex.

Step2: Analyze for adjacent complementary angles

In the given diagrams, if we consider the angles around a point, for question 1, in the left - hand diagram, if we assume that the right - angle formed at a point is divided into two adjacent angles, say ∠FGH and ∠HGI such that ∠FGH + ∠HGI=90°. Let's assume ∠FGH = 41° and ∠HGI = 49°. So a pair of adjacent complementary angles could be ∠FGH and ∠HGI.

Step3: Analyze for adjacent supplementary angles

For question 2, in the right - hand diagram, if we consider a straight - line formed at a point J, two adjacent angles like ∠MJN and ∠NJP where ∠MJN+∠NJP = 180°. Let ∠MJN = 131° and ∠NJP = 49°. So a pair of adjacent supplementary angles is ∠MJN and ∠NJP.

Step4: Analyze for non - adjacent supplementary angles

For question 3, we need two angles that add up to 180° but do not share a common side. In the right - hand diagram, if we consider the angles around point J, ∠LJK and ∠PJM are non - adjacent and ∠LJK+∠PJM = 180°.

Step5: Analyze for non - adjacent complementary angles

For question 4, we need two angles that add up to 90° but do not share a common side. In the left - hand diagram, if we consider the angles formed by the intersection of lines, we can find non - adjacent angles that add up to 90°. For example, if we assume some angle relationships, we might find non - adjacent angles that meet the criteria. But without specific angle measures given precisely, we can't name them exactly. However, conceptually, we are looking for two non - adjacent angles that sum to 90°.

Answer:

1. ∠FGH and ∠HGI (assuming appropriate angle measures in the left - hand diagram)
2. ∠MJN and ∠NJP (in the right - hand diagram)
3. ∠LJK and ∠PJM (in the right - hand diagram)
4. Conceptually, non - adjacent angles that sum to 90° in the left - hand diagram (exact names depend on specific angle measures not given precisely)