Lesson 4.5 Number 6 Use the following diagram to solve problems 6 . Given: $$ \overline{\mathbf{A B}} \| \overline{\mathrm{CD}} $$. What i $$ \mathrm{m} \angle \mathrm{EQF} $$ if $$ \mathrm{m} \angle 1=110^{\circ} $$ and $$ \mathrm{m} \angle 2=135^{\circ} $$ ? Answer format: 150 degrees

Question

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To solve for $$ \mathrm{m} \angle EQF $$ given that $$ \overline{AB} \parallel \overline{CD} $$, and the measures of angles 1 and 2, we can use the properties of parallel lines and transversals.

### Step 1: Identify the relationships between the angles
Since $$ \overline{AB} \parallel \overline{CD} $$, we know that the angles formed by a transversal intersecting these parallel lines have specific relationships.

1. **Angle 1** and **Angle 2** are likely corresponding angles or alternate interior angles, depending on their positions relative to the transversal.

### Step 2: Analyze the angles
- Given $$ \mathrm{m} \angle 1 = 110^\circ $$
- Given $$ \mathrm{m} \angle 2 = 135^\circ $$

### Step 3: Determine $$ \mathrm{m} \angle EQF $$
Assuming $$ \angle EQF $$ is related to either $$ \angle 1 $$ or $$ \angle 2 $$ through the properties of parallel lines, we can analyze the situation:

- If $$ \angle EQF $$ is corresponding to $$ \angle 1 $$, then:
  $$
  \mathrm{m} \angle EQF = \mathrm{m} \angle 1 = 110^\circ
  $$

- If $$ \angle EQF $$ is supplementary to $$ \angle 2 $$ (which is possible if they are on the same side of the transversal), then:
  $$
  \mathrm{m} \angle EQF = 180^\circ - \mathrm{m} \angle 2 = 180^\circ - 135^\circ = 45^\circ
  $$

### Conclusion
Since the problem does not specify the exact position of $$ \angle EQF $$ relative to angles 1 and 2, we need to clarify the relationships. However, if we assume $$ \angle EQF $$ is supplementary to $$ \angle 2 $$, we find:

$$
\mathrm{m} \angle EQF = 45^\circ
$$

If $$ \angle EQF $$ corresponds to $$ \angle 1 $$, then:

$$
\mathrm{m} \angle EQF = 110^\circ
$$

Given the answer format requested, if we assume $$ \angle EQF $$ corresponds to $$ \angle 1 $$:

$$
\mathrm{m} \angle EQF = 110^\circ
$$

Thus, the answer is:

**110 degrees**
$$ \mathrm{m} \angle EQF = 110^\circ $$

Lesson 4.5 Number 6
Use the following diagram to solve problems 6 . Given: . What i
if and ?
Answer format: 150 degrees

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Solución

Step 1: Identify the relationships between the angles

Step 2: Analyze the angles

Step 3: Determine

Conclusion

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Lesson 4.5 Number 6 Use the following diagram to solve problems 6 . Given: . What i if and ? Answer format: 150 degrees