Question

Analyzing Angle Pair Relationships 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

Given:

Parallel lines p and q are cut by transversal r.

m∠3=(3x + 4)° and m∠5=(2x + 11)°.

To find:

The relation between ∠3 and ∠5, then find the measure of angle 5.

Solution:

Parallel lines p and q are cut by transversal r as shown in the below figure.

From the figure it is clear that ∠3 and ∠5 are alternate interior angle. So, the values of these angles are equal.

`m\angle 3=m\angle 5`

`(3x+4)^\circ=(2x+11)^\circ`

`3x+4=2x+11`

Therefore, the required equation to solve for x is
`3x+4=2x+11`.

Isolate variable terms.

`3x-2x=11-4`

`x=7`

The value of x is 7.

Now,

`\angle 5=(2x+11)^\circ`

`\angle 5=(2(7)+11)^\circ`

`\angle 5=(14+11)^\circ`

`\angle 5=25^\circ`

Therefore, the measure of angle 5 is 25°.