Question

Parallel lines p and q are cut by transversal r. On line p where it intersects with line r, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: 1, 2, 4, 3. On line q where it intersects with line r, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: 5, 6, 8, 7.
m∠3 is (3x + 4)° and m∠5 is (2x + 11)°.



Angles 3 and 5 are
.



The equation
can be used to solve for x.



m∠5 =
°

Answer 1

To solve this problem involving parallel lines cut by a transversal, we need to identify the relationship between angles 3 and 5 given their measures.

Since line \( p \) and line \( q \) are parallel and cut by transversal \( r \), angles 3 and 5 are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal.

Thus, we can set up the equation based on the expressions given for angles 3 and 5:

\[
m∠3 = m∠5
\]

Given:
- \( m∠3 = (3x + 4)° \)
- \( m∠5 = (2x + 11)° \)

Setting them equal:

\[
3x + 4 = 2x + 11
\]

Now, we can solve for \( x \):

1. Subtract \( 2x \) from both sides:
\[
3x - 2x + 4 = 11
\]
\[
x + 4 = 11
\]

2. Subtract 4 from both sides:
\[
x = 11 - 4
\]
\[
x = 7
\]

Now, we can find the measure of angle 5 using the value of \( x \):

\[
m∠5 = 2x + 11 = 2(7) + 11
\]
\[
m∠5 = 14 + 11
\]
\[
m∠5 = 25°
\]

In summary:
- Angles 3 and 5 are **corresponding angles**.
- The equation \( 3x + 4 = 2x + 11 \) can be used to solve for \( x \).
- \( m∠5 = 25° \).