Question

in a sports field design, if ∠3 = 3y + 25 and ∠6 = 5y - 15 are alternate interior angles, what is the measure of ∠6 when y = 20?
a. 90 degrees
b. 85 degrees
c. 100 degrees
d. 95 degrees

which angles are supplementary when two parallel lines are intersected by a transversal?
a. corresponding angles
b. alternate exterior angles
c. alternate interior angles

Explanation:

Step1: Substitute y value for ∠6

Given ∠6 = 5y−15 and y = 20. Substitute y into the formula: ∠6=5×20 - 15.

Step2: Calculate the value of ∠6

5×20 - 15=100 - 15 = 95 degrees.

Step3: Recall angle - relationships for second question

When two parallel lines are intersected by a transversal, corresponding angles are congruent, alternate exterior angles are congruent, alternate interior angles are congruent, and same - side interior angles are supplementary. So the given options (a, b, c) are incorrect for supplementary angles.

Answer:

1. d. 95 degrees
2. None of the above (Supplementary angles are same - side interior angles when two parallel lines are intersected by a transversal).