Question

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Answer 1

Answer:

x = 52°

Acute angle = 64°

Step-by-step explanation:

Problem 1:

Since DN bisects <BDW, this means that m<BDN = m<NDW

Thus:

5v - 8 = 4v + 4

Collect like terms

5v - 4v = 8 + 4

v = 12

x = m<BDN = 5v - 8

x = 5v - 8

Plug in the value of v

x = 5(12) - 8

x = 52°

Problem 2:

First, find the value of y

(4y - 44) + (3y + 35) = 180 (linear pair)

4y - 44 + 3y + 35 = 180

7y - 9 = 180

7y = 180 + 9

7y = 189

Divide both sides by 7

y = 27

Acute angle = 4y - 44

Plug in the value of y

Acute angle = 4(27) - 44 = 64°