Question 9

Question 9 Right triangle ABC and right triangle ACD overlap as shown below. Angle DAC measures 20˚ and angle BCA measures 30˚. What are the values of x and y? The students can use a calculator for this problem. Each part of the question (value for x and value for y) is worth one point, so two points total. On the following slides you can see how to solve for each value of x and y.

Question 9 Cont 90 + x + 20 + 30 = 180 140 + x = 180 ______________ This first triangle will be solved for the value of x. Triangles have 180 degrees, when you add all of the degrees together. In this triangle ABC, we know a few values of it. The degree amount at angle B is 90 (the square in the corner means that it is a right angle and right angles are 90). So, when we add up the degrees within this triangle, we have: 90 + x + 20 + 30 = 180. All of those values within that triangle will equal to 180. We then add them together and we get that 140 + x = 180. To solve for x, we subtract 140 from both sides and we get that x = 40. 140 + x = 180 ______________ -140 -140 x = 40

Question 9 Cont 90 + y + 20 + 30 = 180 140 + y = 180 ______________ This first triangle will be solved for the value of y. Triangles have 180 degrees, when you add all of the degrees together. In this triangle ACD, we know a few values of it. The degree amount at angle B is 90 (the square in the corner means that it is a right angle and right angles are 90). So, when we add up the degrees within this triangle, we have: 90 + y + 20 + 30 = 180. All of those values within that triangle will equal to 180. We then add them together and we get that 140 + y = 180. To solve for x, we subtract 140 from both sides and we get that y = 40. 140 + y = 180 ______________ -140 -140 y = 40