Question

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Explanation:

Step1: Identify angle pair for ∠5 & ∠3

∠5 and ∠3 are alternate interior angles (between lines a,b; opposite sides of transversal).

Step2: Find m∠1 using m∠7=75°

∠7 ≅ ∠5 (vertical angles), ∠5 ≅ ∠1 (corresponding angles, a∥b). So m∠1=m∠7=75°.

Step3: Find m∠4 using m∠6=75°

∠6 ≅ ∠4 (alternate interior angles, a∥b). So m∠4=m∠6=75°.

Step4: Solve for x using m∠5=x+10 & m∠4=75°

∠5 ≅ ∠4 (alternate interior angles, a∥b). Set x+10=75 → x=65.

Answer:

a. Alternate interior angles
b. 75°
c. 75°
d. 65