The two corresponding angles formed by the intersection of two parallel lines by a transversal are (3x-20°) and (5x −60°). Then, the value of (4x +30°) is :

Q: The two corresponding angles formed by the intersection of two parallel lines by a transversal are (3x-20°) and (5x −60°). Then, the value of (4x +30°) is :

To solve the problem, we need to determine the value of $4x + 30^\circ$ given that the two corresponding angles formed by the intersection of two parallel lines by a transversal are $3x - 20^\circ$ and $5x - 60^\circ$. ### Explanation: 1. **Understanding Corresponding Angles:** - When two parallel lines are intersected by a transversal, corresponding angles are equal. Therefore, we can set the two given angles equal to each other: \[ 3x - 20^\circ = 5x - 60^\circ \] 2. **Solving the Equation:** - Rearrange the equation to solve for $x$: \[ 3x - 20 = 5x - 60 \] - Subtract $3x$ from both sides: \[ -20 = 2x - 60 \] - Add 60 to both sides: \[ 40 = 2x \] - Divide by 2: \[ x = 20 \] 3. **Finding the Value of $4x + 30^\circ$:** - Substitute $x = 20$ into the expression $4x + 30^\circ$: \[ 4x + 30^\circ = 4(20) + 30 = 80 + 30 = 110^\circ \] ### Conclusion: - The value of $4x + 30^\circ$ is $110^\circ$, which corresponds to Option 3. ### Explanation of Incorrect Options: 1. **Option 1: 150°** - If $4x + 30^\circ$ were 150°, it would imply a different value of $x$, which contradicts the solution derived from the equality of corresponding angles. 2. **Option 2: 90°** - A value of 90° for $4x + 30^\circ$ would also imply a different $x$, inconsistent with the equality of the given angles. 3. **Option 4: 130°** - Similarly, a value of 130° would not satisfy the equation derived from the corresponding angles being equal. Thus, the correct answer is indeed Option 3, $110^\circ$, as it is the only value consistent with the conditions given in the problem.

Question

Accepted Answer

To solve the problem, we need to determine the value of $4x + 30^\circ$ given that the two corresponding angles formed by the intersection of two parallel lines by a transversal are $3x - 20^\circ$ and $5x - 60^\circ$.

### Explanation:

1. **Understanding Corresponding Angles:**
   - When two parallel lines are intersected by a transversal, corresponding angles are equal. Therefore, we can set the two given angles equal to each other:
     $$
     3x - 20^\circ = 5x - 60^\circ
     $$

2. **Solving the Equation:**
   - Rearrange the equation to solve for $x$:
     $$
     3x - 20 = 5x - 60
     $$
   - Subtract $3x$ from both sides:
     $$
     -20 = 2x - 60
     $$
   - Add 60 to both sides:
     $$
     40 = 2x
     $$
   - Divide by 2:
     $$
     x = 20
     $$

3. **Finding the Value of $4x + 30^\circ$:**
   - Substitute $x = 20$ into the expression $4x + 30^\circ$:
     $$
     4x + 30^\circ = 4(20) + 30 = 80 + 30 = 110^\circ
     $$

### Conclusion:

- The value of $4x + 30^\circ$ is $110^\circ$, which corresponds to Option 3.

### Explanation of Incorrect Options:

1. **Option 1: 150°**
   - If $4x + 30^\circ$ were 150°, it would imply a different value of $x$, which contradicts the solution derived from the equality of corresponding angles.

2. **Option 2: 90°**
   - A value of 90° for $4x + 30^\circ$ would also imply a different $x$, inconsistent with the equality of the given angles.

3. **Option 4: 130°**
   - Similarly, a value of 130° would not satisfy the equation derived from the corresponding angles being equal.

Thus, the correct answer is indeed Option 3, $110^\circ$, as it is the only value consistent with the conditions given in the problem.