Question

Items 2-4. Points P, Q, and Sare

Answer 1

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°