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4 years ago

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

Mathematics

1 answer:

Ivanshal [37]4 years ago

8 0

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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LuckyWell [14K]

The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:

R2: Definition of corresponding angles
R3: Corresponding angles postulate
R5: Supplement Postulate
S7: m∠1 + m∠3 = m∠2 + m∠3
S8: m∠1 + m∠3 = 180° (∠1 is supplementary to ∠3)

<h3>What are Supplementary Angles?</h3>

Supplementary angles, when added together will give us a sum of 180°.
Linear pair angles and corresponding angles are supplementary.

Thus, to prove that ∠1 is supplementary to ∠3:

We are given that lines m and n are parallel.

∠1 and ∠3 are corresponding angles.

So therefore, ∠1 = ∠3 by the corresponding angles postulate.

∠2 and ∠3 are linear pair, their sum therefore equals 180° based on the definition of supplementary angles.

Based on the substitution property, we have the following:

m∠2 + m∠3 = m∠1 + m∠3

m∠1+m∠3=180°

Therefore, ∠1 is supplementary to ∠3 based on the definition of supplementary.

The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:

R2: Definition of corresponding angles
R3: Corresponding angles postulate
R5: Supplement Postulate
S7: m∠1 + m∠3 = m∠2 + m∠3
S8: m∠1 + m∠3 = 180° (∠1 is supplementary to ∠3)

Learn more about supplementary angles on:

brainly.com/question/8992900

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