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1.07 Exploring Angles

 

Work the following practice examples to see how you can solve problems using what you have learned about angles.

Use the drawing below to answer questions 1 through 5.
Triangle A B C. Point D lies on Segment A B. Segment D C is intersected by segment B E in the interior of the triangle. Angle 1 is another name for angle A D C, Angle 2 is another name for angle B D C. Angle 3 is another name for angle B C D. Angle 4 is another name for angle A C D.
1. List all the angles that have D as a vertex.
2. Name a straight angle in the drawing above.
3. Does Angle B E C appear to be acute, right, obtuse, or straight?
Explain your answer.
4. How many angles have C as their vertex? Name them.
5. Name a point that meets the following criteria:
  1. A point in the interior of Angle A C B.
  2. A point in the exterior of Angle D B C.
  3. A point on Angle D B C.
Use the figure below to answer questions 6 and 7.
    Acute angle G B F. Another name for this angle is angle 3
6. Name the vertex of Angle 3.
7. Name the sides of Angle 3.
8. Study a corner of a room where two walls and the ceiling meet. (Be sure to use a corner of a room where the walls appear to be coming to form 90 degree angles.) How many right angles are formed at the corner?
Use the figure below to answer questions 9 through 12. Determine whether the angle named appears to be acute, obtuse, or a straight angle.
Overlapping triangles A B E and C B D. Angle C is also angle 1. Angle C E A is angle 2. Angle A E B is angle 3. Angle B is angle 4. Angle C F E is angle 5. Angle E F D is angle 6. Angle A F D is angle 7. Angle A D F is also angle 8. Angle A is angle 9. Angle C D B is angle 10.
9. angle 6 or angle D F E
10. angle 4 or angle A B C
11. angle 5 or angle C F E
12. angle A D B

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