Geometry - Lines Cut by a Transversal assignment

The measure of angle 1 is (3x + 10)° and the measure of angle 4 is (4x - 15)°. What is the measure of angle 7?

95

Given: w ∥ x and y is a transversal.Prove: ∠3 and ∠5 are supplementary. Use the drop-down menus to complete the proof. Given that w ∥ x and y is a transversal, we know that ∠1 ≅∠5 by the ________. Therefore, m∠1 = m ∠5 by the definition of congruent. We also know that, by definition, ∠3 and ∠1 are a linear pair so they are supplementary by the _________. By the _________, m∠3 + m ∠1 = 180. Now we can substitute m∠5 for m∠1 to get m∠3 + m∠5 = 180. Therefore, by the definition of supplementary angles, ∠3 and ∠5 are supplementary.

1. corresponding angles theorem 2. linear pair postulate 3. definition of supplementary angles

What is the value of x?

70

Given: Lines p and q are parallel and r is a transversal. Prove: ∠2 ≅ ∠7 Which statements could complete the proof?

A: Angle 2 is congruent to angle 3 B: Angle 3 is congruent to angle 7

m∠6 is (2x - 5)° and m∠8 is (x + 5)°. What is m∠3?

115

In the diagram, m∠3 = 120° and m∠12 = 80°. Which angle measures are correct? Check all that apply

a, b, d, f

Given: a and b are parallel and c is a transversal. Prove: ∠2 ≅ ∠7 Use the drop-down menus to complete the paragraph proof showing that alternate interior angles are congruent.We know that lines a and b are parallel and that line c is a transversal because that is given. We can tell that angles 2 and 5 are congruent because ________ angles are congruent. Angles 5 and 7 are congruent because ________ angles by parallel lines cut by a transversal are congruent. Therefore, angles 2 and 7 are congruent based on the ________.

1. vertical 2. corresponding 3. transitive property

A section of wall is being framed. A model of the framing work is shown below. Which best describes the relationship between the 125° angle and angle A?

a. They are same side interior angles. Angle A measures 55°.