Triangles, Angles, Lines: I need a challenge! 1. If DY bisects right angle ABC, what is the measure of angle ABD? Tara Patel 6/17/14 10:41 AM
Comment [1]: 135 A
Y
B
C
D
2. Two angles are supplementary. The larger angle exceeds 7 times the smaller one by 4 degrees. Find the measure of each angle. 3. Two supplementary angles are in the ratio 11:7. Find the measure of each. 4. The vertices of triangle ABC are A(1, -­‐2), B (4, 0) and C (2, 2). What is the area of this triangle? 5. 2 rays
1 angle
3 rays
2 angles
4 rays
____ angles
5 rays
____ angles
a) complete the blanks in the diagram above b) Study the pattern in the four cases shown, and predict the number of angles formed by six noncollinear rays that have the same endpoint c) Which of the expressions below gives the number of angles formed by n noncollinear rays that have the same endpoint? Tara Patel 6/17/14 1:55 PM
Comment [2]: Equation: (x) + (7x+4) = 180 Larger angle: 158 Smaller angle: 22 Tara Patel 6/17/14 1:58 PM
Comment [3]: 110 and 70 (equation should be 11x+7x=180) Tara Patel 6/17/14 11:41 AM
Comment [4]: 5. The simplest way to solve this is to make a rectangle around the triangle, and then subtract each of the corner triangles. (The rectangle is 3x4, so area 12. The corner triangle areas are 2, 2, and 3. Tara Patel 6/17/14 1:16 PM
Comment [5]: a)6; 10 b)15 c)n(n-­‐1)/2 n −1 2n − 3 n 2 − 3 n(n −1)
2
6. AL is an angle bisector of angle KAT. Find the value of x given that angle 2 = x + 12 and angle 3 = 6x – 20. K
Tara Patel 6/17/14 1:19 PM
Comment [6]: x=22 L
3
S
7. 2
1
A
T
Find the values of x and y. x + 2y
2x + y
Tara Patel 6/17/14 1:22 PM
Comment [7]: To solve this problem, you need to write 2 different equations: (x + 2y) + (2x + y) + 90 = 180, and (2x + y) = 125. Then, use substitution to solve the equations. ANSWERS: x = 25; y = 5 125°
8. The base of a triangle and 1 meter longer than its height. If the area of the triangle is 210 square meters, what is its height? 9. The diagram shows Kara’s watch. If Kara cannot go home until 4:15, how many degrees must the hour hand travel before she can go home? Tara Patel 6/17/14 1:41 PM
Comment [8]: 20 cm Tara Patel 6/17/14 2:00 PM
Comment [9]: 20 degrees 12
3
9
6