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Use the Angle Addition Postulate to find the value of x, then find the measure of the indicated angle.

Use the Angle Addition Postulate to find the value of x, then find the measure of-example-1
User Illia Tereshchuk
by
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1 Answer

22 votes
22 votes
Finding unkown angles

We know m∠NBR can be written in two ways:

m∠NBR = 17x + 8 [given]

and

m∠NBR = (12x + 4) + 42 [observed in the drawing]

Then

17x + 8 = (12x + 4) + 42

17x + 8 = 12x + 46

Using this formula we can find x- value

Step 1

Rearranging the terms so the terms with the unkown variable x are on the left side and the other ones on the right side:

17x + 8 = 12x + 46

substracting 12x both sides

-12x + 17x + 8 = 46

substracting 8 both sides

-12x + 17x = - 8 + 46

5x = 38

Step 2

Solving the equation for x:

5x = 38

dividing by 5 both sides

5x/5 = 38/5

x = 7.6

Answer 1: x = 7.6

Now we want to find m∠NBS

It is given that

m∠NBS = 12x + 4

to find it we just replace x by 7.6:

m∠NBS = 12 · 7.6 + 4

m∠NBS = 91.2 + 4

m∠NBS = 95.2

Answer 2: m∠NBS = 95.2

User Brevleq
by
2.8k points
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