Question

1. Roger Federer has a dream about a new kind of tennis racket. He wants the parallel catgut strings to intersect at an angle of 135 degrees. Help Roger calculate what the rest of the angles will be on his new tennis racket.

a) On string number one, we know the angle created with string number three is 135 degrees. What is the measurement of angle A? Explain or defend your answer. (3 points)



b) What is the measurement of angle B? Explain or defend your answer. (3 points)



c) If Roger has created his tennis racket according to plan, what should be the measurement of angle C? Explain or defend your answer. (3 points)

Answer 1

a) The angle A and the angle of 135° are adjacent angles (to one side of a straight line), then they must be supplementary and they must add 180°:
A+135°=180°
Solving for A:
A+135°-135°=180°-135°
A=45°

Answer: The measurement of angle A is 45°.

b) The angle B is opposite by the vertex to the angle of 135°, and angles opposite by the vertex are congruents, then the measurement of angle B is 135°

Answer: The measurement of angle B is 135°.

c) Since lines 1 and 2 are parallel, the corresponding angles must be congruent. The angles A and C are corresponding, therefore they must be congruent, therefore the measure of the angle C must be equal to the measure of the angle A of 45°

Answer: The measurement of angle C is 45°.

Answer 2

a. We can determine the measurement of angle A by considering that angle A and the 135-degree angle are supplementary. Supplementary angles are angles in a straight line and together they add up to 180 degrees. So, to find A, we just subtract 135 degrees from 180.


`A=180-135=45`

ANSWER: The measure of angle A is 45 degrees.

b. Similarly, we can get the measurement of angle B by considering that A and B are supplementary angles. We can therefore get its measurement by subtracting 45 from 180.


`B=180-45=135`

Additionally, we can also use the concept of vertical angles. Vertical angles are angles opposite each other in any intersecting lines. These angles have equal measurements. We know for a fact that opposite angle B is 135 degrees therefore it must also be 135 degrees.

ANSWER: The measure of angle B is 135 degrees.

c. Since the two strings are parallel, we can see some similarities between the angles in string 1 and string 2. We can notice that the measure of angle C should just be the same as the measure of angle A since both angles are located at the same location of the string. Therefore, angle C will also be equal to 45 degrees.

ANSWER: The measure of angle C is 45 degrees.