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1. BD bisects
2. < RQT is a straight angle. What are m
3.

1. BD bisects 2. < RQT is a straight angle. What are m 3.-example-1

1 Answer

3 votes

Answer:

16.:

x = 5

m ∠ABC = 60°

17.:

m ∠RQS is 102°.

m ∠TQS is 78°

18.:

m ∠EFG = 75°

m ∠GFH = 105°

Explanation:

16.:

  • An angle bisector splits one angle into two equal angles.
  • Thus, ∠ABD + ∠CBD = ∠ABC and ∠ABD = ∠CBD.

Solving for x:

We can now find x by setting angles ABD and CBD equal to each other:

ABD = CBD

(7x - 5 = 5x + 5) + 5

(7x = 5x + 10) - 5x

(2x + 10) / 2

x = 5

Thus, x = 5.

Finding the measure of ∠ABC:

Now we can find the measure of ∠ABC by plugging in 5 for x in either 7x - 5 or 5x + 5 and multiplying by 2. Let's do 7x - 5:

m∠ABC = 2 * (7(5) - 5)

m ∠ABC = 2 * (35 - 5)

m ∠ABC = 2 * (30)

m ∠ABC = 60

Thus, the measure of ∠ABC is 60°.

17.:

  • A straight angle is 180°.
  • Thus, the measure of ∠RQT is 180.

Solving for x:

Since RQS + TQS = 180°, we can first find x by setting the sum of the two angles equal to 180:

14x + 4 + 11x + 1 = 180

(14x + 11x) + (4 + 1) = 180

(25x + 5 = 180) - 5

(25x = 175) / 25

x = 7

Thus, x = 7

Finding m∠RQS:

Now we plug in 7 for x in 14x + 4 to find m ∠RQS:

m ∠RQS = 14(7) + 4

m ∠RQS = 98 + 4

m ∠RQS = 102

Thus, m ∠RQS is 102°.

Finding m ∠TQS:

Since m ∠RQS + m ∠TQS = 180°, we can find m ∠TQS by subtracting 102 from 180:

m ∠RQS + m ∠TQS = 180

m ∠TQS = 180 - m ∠RQS

m ∠TQS = 180 - 102

m ∠TQS = 78

Thus, m ∠TQS is 78°

18.:

  • A linear pair is defined as two adjacent angles that form a straight angle.
  • This means that the sum of a linear pair is 180°.

Finding n:

We can first find n by setting the sum of m ∠EFG and m ∠GFH equal to 180°:

m ∠EFG + m ∠GFH = 180°

3n + 24 + 4n + 37 = 180

(3n + 4n) + (24 + 37) = 180

(7n + 61 = 180) - 61

(7n = 119) / 7

n = 17

Thus, n = 17.

Finding m ∠EFG:

Now we can find m ∠EFG by plugging in 17 for n in 3n + 24:

m ∠EFG = 3(17) + 24

m ∠EFG = 51 + 24

m ∠EFG = 75

Thus, m ∠EFG = 75°.

Finding m ∠GFH:

Now we can find m ∠GFH by plugging in 17 for n in 4n + 37:

Now we can find m ∠GFH by plugging in 17 for n in 4n + 37:

m ∠GFH = 4(17) + 37

m ∠GFH = 68 + 37

m ∠GFH = 105

Thus ,m ∠GFH = 105°.

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