Answer:
N = 40°
V = 13°
W = 95°
X = 53°
Y = 95°
Z = 32°
A = 28.60316
B = 18.28946
Explanation:
The sum of the angles of any triangle is 180°
You don't have to calculate the angles in order.
Angle Measurements
N) The lower triangle is composed of angles n, y, and (180 - 135)° - think supplementary angles.
n + y + 180° - 135° = 180°
n + y = 135°
n + 95° = 135°
n = 40°
V) The overall triangle is composed of angles y, z, n, and v.
The values for y, z, and n are 95°, 32°, and 40°, respectively.
y + z + n + v = 180°
v + 95° + 32° + 40° = 180°
v + 167° = 180°
v = 13°
W) y and w are corresponding angles because their respective lines are parallel, so their angle measurements are equal.
y = w = 95°
X) 53° and x are vertical angles, their measurements are equal.
Y) A full circle is 360°. So the sum of the angles at a single point is 360°. 53, 32, x, z, y, and the angle opposite y, add up to 360°. y and the angle opposite it are equal because they are vertical angles.
53 + 32 + 53 + 32 + 2y = 360
170 + 2y = 360
2y = 190
y = 95°
Z) 32° and z are vertical angles, their measurements are equal.
Side Lengths
Use the law of sines to calculate the side lengths. Each angle corresponds to the side length direcly opposite it (not adjacent).
Law of Sines
The A is the angle, and a is the corresponding side length. This law shows the relationship between angle and side length to be equal for every side. Note that the Law of Sines works for any triangle.
A) Use Law of Sines with angles and side lengths that correspond to A.
Substitute in all known values, z and y.
Cross-multiply.
B) Do the same thing as for A, but use angles and side lengths that correspond to B.
Substitute 40° for n and cross-multiply.
