E\% Lesson 4.5 Number 5 Use the following dogrom to solve the problem, given that $$ \overline{A B} \| \overline{C D} $$ and fie $$ \ell: $$ the tronsversel Jusify your onswers using angle relationships in parollel fres Interseaded by a transversal. What is $$ \mathrm{m} \angle 1 $$ if $$ \mathrm{m} \angle 1=11 \mathrm{x}+35 $$ and $$ \mathrm{m} \angle 4=\mathrm{x}+1 $$ ? Answer format: 150 degress

Question

UpStudy AI · Accepted Answer

To determine the measure of $$ \angle 1 $$, let's analyze the given information step by step.

### Given:
- $$ \overline{AB} \parallel \overline{CD} $$
- Line $$ \ell $$ is a transversal intersecting these parallel lines.
- $$ \mathrm{m} \angle 1 = 11x + 35 $$
- $$ \mathrm{m} \angle 4 = x + 1 $$

### Understanding the Angle Relationships:
Since $$ \overline{AB} \parallel \overline{CD} $$ and $$ \ell $$ is a transversal, angles formed can be related as **same-side interior angles**, which are **supplementary**. This means:

$$
\mathrm{m} \angle 1 + \mathrm{m} \angle 4 = 180^\circ
$$

### Setting Up the Equation:
$$
(11x + 35) + (x + 1) = 180
$$

### Solving for $$ x $$:
$$
12x + 36 = 180
$$
$$
12x = 180 - 36
$$
$$
12x = 144
$$
$$
x = 12
$$

### Calculating $$ \mathrm{m} \angle 1 $$:
$$
\mathrm{m} \angle 1 = 11x + 35 = 11(12) + 35 = 132 + 35 = 167^\circ
$$

### Conclusion:
There appears to be a discrepancy between the calculated value (167°) and the expected answer format (150°). It's possible that there might be additional information or a different angle relationship intended in the problem. However, based on the provided information and standard angle relationships:

**The measure of $$ \angle 1 $$ is 167 degrees.**
$$ \mathrm{m} \angle 1 = 167^\circ $$

E%

Lesson 4.5 Number 5
Use the following dogrom to solve the problem, given that and fie the tronsversel Jusify your onswers using angle relationships in parollel fres Interseaded by a transversal. What is if and ?
Answer format: 150 degress

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E% Lesson 4.5 Number 5 Use the following dogrom to solve the problem, given that and fie the tronsversel Jusify your onswers using angle relationships in parollel fres Interseaded by a transversal. What is if and ? Answer format: 150 degress