Question

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Answer 1

Answer:

1. a. Q° = 95°

b. a = 20.3; b = 19.3

2. p = 36; q = 14.4

Step-by-step explanation:

Question 1:

Recall: The Exterior Angle Theorem of a Triangle states that the size of the exterior angle of a triangle equals the sum of the two sizes of the two opposite angles of the triangle.

a. Based on the theorem,

Q° = 41° + 54° = 95°

b.

✔️122° = 4a + 2a (exterior angle theorem)

122 = 6a

Divide both sides by 6

122/6 = a

a = 20.3

✔️122° + 3b = 180° (angles on a straight line)

3b = 180 - 122

3b = 58

b = 58/3

b = 19.3

Question 2:

Recall: Opposite angles of a parallelogram are equal while adjacent/consecutive angles are supplementary.

✔️2p + 3p = 180° (adjacent angles)

5p = 180

p = 180/5

p = 36

✔️2p = 5q (opposite angles)

Plug in the value of p

2(36) = 5q

72 = 5q

72/5 = q

q = 14.4