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part 3 – practice use diagram 1 to answer the questions below 1. if the…

Question

part 3 – practice
use diagram 1 to answer the questions below

  1. if the ( mangle 8 = 47^circ ), find ( mangle 12 ).
  2. if the ( mangle 7 = 125^circ ), find ( mangle 6 ).
  3. if the ( mangle 6 = 84^circ ), find ( mangle 12 ).
  4. if the ( mangle 14 = 38^circ ), find ( mangle 13 ).
  5. if the ( mangle 9 = 143^circ ), find ( mangle 12 ).
  6. if the ( mangle 8 = 52^circ ), find ( mangle 6 ).
  7. if the ( mangle 5 = 90^circ ), find ( mangle 1 ).
  8. if the ( mangle 9 = 135^circ ), find ( mangle 13 ).

Explanation:

Response

To solve these angle - related problems, we assume that the diagram involves parallel lines cut by a transversal. We will use the properties of corresponding angles, alternate - interior angles, alternate - exterior angles, and supplementary angles (angles that add up to \(180^{\circ}\)) as needed.

Question 1: If \(m\angle8 = 47^{\circ}\), find \(m\angle12\)

Step 1: Identify the angle relationship

\(\angle8\) and \(\angle12\) are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are equal.

Step 2: Determine the measure of \(\angle12\)

Since \(\angle8\) and \(\angle12\) are corresponding angles, \(m\angle12=m\angle8\)
Given \(m\angle8 = 47^{\circ}\), then \(m\angle12 = 47^{\circ}\)

Question 2: If \(m\angle7 = 125^{\circ}\), find \(m\angle6\)

Step 1: Identify the angle relationship

\(\angle7\) and \(\angle6\) are supplementary angles (they form a linear pair). So, \(m\angle7 + m\angle6=180^{\circ}\)

Step 2: Solve for \(m\angle6\)

We know that \(m\angle7 = 125^{\circ}\), so we can rewrite the equation as \(m\angle6=180^{\circ}-m\angle7\)
Substitute \(m\angle7 = 125^{\circ}\) into the equation: \(m\angle6 = 180^{\circ}- 125^{\circ}=55^{\circ}\)

Question 3: If \(m\angle6 = 84^{\circ}\), find \(m\angle12\)

Step 1: Identify the angle relationship

First, \(\angle6\) and \(\angle8\) are supplementary (linear pair), so \(m\angle6 + m\angle8 = 180^{\circ}\). Then \(\angle8\) and \(\angle12\) are corresponding angles.
First, find \(m\angle8\): \(m\angle8=180^{\circ}-m\angle6\)
Substitute \(m\angle6 = 84^{\circ}\), we get \(m\angle8 = 180^{\circ}-84^{\circ}=96^{\circ}\)
Since \(\angle8\) and \(\angle12\) are corresponding angles, \(m\angle12=m\angle8\)
So \(m\angle12 = 96^{\circ}\)

Question 4: If \(m\angle14 = 38^{\circ}\), find \(m\angle13\)

Step 1: Identify the angle relationship

\(\angle14\) and \(\angle13\) are supplementary angles (linear pair), so \(m\angle14 + m\angle13=180^{\circ}\)

Step 2: Solve for \(m\angle13\)

We know \(m\angle14 = 38^{\circ}\), so \(m\angle13=180^{\circ}-m\angle14\)
Substitute \(m\angle14 = 38^{\circ}\) into the equation: \(m\angle13=180^{\circ}-38^{\circ}=142^{\circ}\)

Question 5: If \(m\angle9 = 143^{\circ}\), find \(m\angle12\)

Step 1: Identify the angle relationship

\(\angle9\) and \(\angle12\) are supplementary angles (same - side interior angles, assuming parallel lines). So \(m\angle9 + m\angle12=180^{\circ}\)

Step 2: Solve for \(m\angle12\)

We know \(m\angle9 = 143^{\circ}\), so \(m\angle12=180^{\circ}-m\angle9\)
Substitute \(m\angle9 = 143^{\circ}\) into the equation: \(m\angle12=180^{\circ}-143^{\circ}=37^{\circ}\)

Question 6: If \(m\angle8 = 52^{\circ}\), find \(m\angle6\)

Step 1: Identify the angle relationship

\(\angle8\) and \(\angle6\) are supplementary angles (linear pair), so \(m\angle8 + m\angle6=180^{\circ}\)

Step 2: Solve for \(m\angle6\)

We know \(m\angle8 = 52^{\circ}\), so \(m\angle6=180^{\circ}-m\angle8\)
Substitute \(m\angle8 = 52^{\circ}\) into the equation: \(m\angle6=180^{\circ}-52^{\circ}=128^{\circ}\)

Question 7: If \(m\angle5 = 90^{\circ}\), find \(m\angle1\)

Step 1: Identify the angle relationship

\(\angle5\) and \(\angle1\) are corresponding angles (assuming parallel lines cut by a transversal). So \(m\angle1=m\angle5\)

Step 2: Determine the measure of \(\angle1\)

Given \(m\angle5 = 90^{\circ}\), then \(m\angle1 = 90^{\circ}\)

Question 8: If \(m\angle9 = 135^{\circ}\), find \(m\angle13\)

Step 1: Identify the angle relationship

\(\angle9\) and \(\angle13\) are co…

Answer:

s:

  1. \(m\angle12=\boldsymbol{47^{\circ}}\)
  2. \(m\angle6=\boldsymbol{55^{\circ}}\)
  3. \(m\angle12=\boldsymbol{96^{\circ}}\)
  4. \(m\angle13=\boldsymbol{142^{\circ}}\)
  5. \(m\angle12=\boldsymbol{37^{\circ}}\)
  6. \(m\angle6=\boldsymbol{128^{\circ}}\)
  7. \(m\angle1=\boldsymbol{90^{\circ}}\)
  8. \(m\angle13=\boldsymbol{135^{\circ}}\)