During the summer, Victoria plays soccer and takes swim and piano lessons. Each swim lesson is 15 minutes shorter than a soccer practice. Each piano lesson is twice as long as a soccer practice. Victoria has soccer three times a week, swimming four times a week, and piano twice a week. She spends a total of 435 minutes each week doing these three activities a week. Write an equation that represents this situation. How long is one session of each activity?

(a) AB = 13

(b) m∠F = 30°

Step-by-step explanation:

(a) The triangle shown is an equilateral triangle, meaning all of its sides are the same length. We know this to be true because all of its angles are the same - 60°. So, if one side is 13, we know that all the sides have a measure of 13, and can thus say that AB = 13.

(b) In this triangle, the lines coming from angle E are the same length. Because of this, points F and D have the same measure. We already know the value of one point - E is 120. If all the angles in a triangle add up to 180, and we already know 120, we know that F and D have to have a value that, doubled, equals 60, since 180 - 120 is 60. 30 doubled is 60, so we know that the value of F is 30.

If you have any further questions or need clarification, let me know!