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Items 2-4. Points P, Q, and Sare
collinear.
(3x - 5)
0
(x + 1)
s
2. What is the value of x?
3. What is m ZPQR?
will
11. M
4. If a ray QT bisects ZRQS, what
will be the measure of one of the
resulting angles?
m
of
5. Points L, M, and N are collinear.
You are given LM = 5 and LN = 17.
What is a possible value of MN?
Flb
6. Ray BD bisects ZABC so that
mZDBC = x + 6 and
mZABD = 2x - 12. What is x?

Items 24 Points P Q and Sare collinear 3x 5 0 x 1 s 2 What is the value of x 3 What is m ZPQR will 11 M 4 If a ray QT bisects ZRQS what will be the measure of o class=

Respuesta :

mhanifa

Answer:

See below

Step-by-step explanation:

2......................

∠PQR and ∠RQS are supplementary, which add up 180°

  • ∠PQR = 3x - 5
  • ∠RQS = x + 1

Sum:

  • 3x - 5 + x + 1 = 180
  • 4x - 4 = 180
  • 4x = 184
  • x = 46°

3......................

  • ∠PQR = 3x - 5 = 3*46° - 5° = 138° - 5° = 133°

4......................

From the picture and the value of x we got above:

  • ∠RQS = x + 1 = 46 + 1= 47°

QT bisects ∠RQS and we get two equal angles

Each will measure:

  • 47°/2 = 23.5°

5......................

LM = 5, LN = 17, MN = ?

If L is between M and N, then

  • MN = LM + LN = 5 + 17 = 22

M is between L and N, then

  • MN = LN - LM = 17 - 5 = 12

5......................

Ray BD bisects ∠ABC, then formed angles are equal:

  • m∠DBC = x + 6
  • m∠ABD = 2x - 12

m∠DBC = m∠ABD

  • x + 6 = 2x - 12
  • 2x - x =6 + 12
  • x = 18°

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