2.05 Adjacent and Congruent Angles

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Answer the following questions concerning adjacent and congruent angles.

Questions 1 - 6 refer to this image.

1. If m∠STW = 95° and m∠WTK = 39°, find the measure of ∠STK.
   1. 56°
   2. 95°
   3. 39°
   4. 134°

   Answer: d. 134°

2. Which angle is adjacent to ∠WTK?
   1. ∠WTK
   2. ∠RTS
   3. ∠STW
   4. ∠RTK

   Answer: c. STW

3. ∠RTS is congruent to ∠KTR. If m∠RTS = (2x + 7)° and m∠KTW = (5x - 5)°, solve for x.
   1. 4
   2. 1
   3. 44
   4. 0.5

   Answer: a. 4

4. ∠RTS is congruent to ∠KTW. If m∠KTW = 44°, find the measure of ∠RTS.
   1. 44°
   2. 36°
   3. 144°
   4. cannot be determined

   Answer: a. 44°

5. If m∠STW = (3x + 11)°. m∠WTK = 40°, and m∠STK = 156°, use an equation and solve for x.
   1. 35
   2. 105
   3. 9
   4. 1

   Answer: a. 35

6. If the sum of all three angles is 180° and ∠RTS is congruent to ∠KTR, and m∠STW = 100°, find m∠RTS
   1. 80°
   2. 40°
   3. 39°
   4. 44°

   Answer: b. 40°



Questions 7 - 6 refer to this image.

7. If ray BD is an angle bisector for ∠ABC, then solve for ∠ABD.
   1. 164°
   2. 16°
   3. 100°
   4. 132°

   Answer: a. 164°

8. Find the sum of the adjacent angles, ∠DBC and ∠CBE
   1. 164°
   2. 16°
   3. 100°
   4. 132°

   Answer: a. 164°

9. Find the sum of the adjacent angles, ∠DBC and ∠CBE
   1. 164°
   2. 10°
   3. 132°
   4. 68°

   Answer: a. 132°

10. If BD is an angle bisector, find the sum of all three adjacent angles.
    1. 164°
    2. 64°
    3. 16°
    4. 68°

    Answer: a. 164°

11. If m∠ABE = 170°, then let m∠ABD = x and solve for x.
    1. 132°
    2. 170°
    3. 38°
    4. none of these

    Answer: a. 38°