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:

To solve these angle - related problems, we assume that the diagram involves parallel lines cut by a transversal (or has vertical angles, supplementary angles, corresponding angles, alternate interior angles, etc. relationships). We will solve each problem one by one:

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

Step 1: Identify the relationship

Assuming that \(\angle8\) 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 corresponding angles are equal, if \(m\angle8 = 47^{\circ}\), then \(m\angle12=m\angle8 = 47^{\circ}\)

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

Step 1: Identify the relationship

\(\angle7\) and \(\angle6\) are supplementary angles (they form a linear pair, so their sum is \(180^{\circ}\)).

Step 2: Calculate \(m\angle6\)

We know that \(m\angle7 + m\angle6=180^{\circ}\). Substituting \(m\angle7 = 125^{\circ}\), we get \(m\angle6=180^{\circ}- 125^{\circ}=55^{\circ}\)

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

Step 1: Identify the relationship

Assuming that \(\angle6\) and \(\angle12\) are alternate interior angles (when two parallel lines are cut by a transversal, alternate interior angles are equal).

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

Since alternate interior angles are equal, \(m\angle12=m\angle6 = 84^{\circ}\)

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

Step 1: Identify the relationship

\(\angle14\) and \(\angle13\) are supplementary angles (they form a linear pair, so their sum is \(180^{\circ}\)).

Step 2: Calculate \(m\angle13\)

We know that \(m\angle14 + m\angle13=180^{\circ}\). Substituting \(m\angle14 = 38^{\circ}\), we get \(m\angle13=180^{\circ}-38^{\circ} = 142^{\circ}\)

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

Step 1: Identify the relationship

\(\angle9\) and \(\angle12\) are supplementary angles (they are same - side interior angles, and if the lines are parallel, same - side interior angles are supplementary).

Step 2: Calculate \(m\angle12\)

We know that \(m\angle9 + m\angle12=180^{\circ}\). Substituting \(m\angle9 = 143^{\circ}\), we get \(m\angle12=180^{\circ}-143^{\circ}=37^{\circ}\)

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

Step 1: Identify the relationship

\(\angle8\) and \(\angle6\) are supplementary angles (they form a linear pair, so their sum is \(180^{\circ}\)).

Step 2: Calculate \(m\angle6\)

We know that \(m\angle8 + m\angle6=180^{\circ}\). Substituting \(m\angle8 = 52^{\circ}\), we get \(m\angle6=180^{\circ}-52^{\circ}=128^{\circ}\)

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

Step 1: Identify the relationship

\(\angle5\) and \(\angle1\) are corresponding angles (when two parallel lines are cut by a transversal, corresponding angles are equal).

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

Since corresponding angles are equal, \(m\angle1=m\angle5 = 90^{\circ}\)

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

Step 1: Identify the relationship

\(\angle9\) and \(\angle13\) are corresponding angles (when two parallel lines are cut by a transversal, corresponding angles are equal).

Step 2: Determine the measure of \(\angle13\)

Since corresponding angles are equal, \(m\angle13=m\angle9 = 135^{\circ}\)

Answer:

s:

1. \(m\angle12=\boldsymbol{47^{\circ}}\)
2. \(m\angle6=\boldsymbol{55^{\circ}}\)
3. \(m\angle12=\boldsymbol{84^{\circ}}\)
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. \(m\angle13=\boldsymbol{135^{\circ}}\)