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Find the values of x, y, and z. The diagram is not to scale.
Triangle A B C is drawn with point D on side B C. A segment is drawn from A to D. Angle A C D measures 63 degrees. Angle C A D measures 36 degrees. Angle D A B measures 13 degrees. Angle C D A measures x degrees. Angle C B A measures y degrees. Angle A D B measures z degrees.
To find the values of x, y, and z, we can use the fact that the angles in a triangle add up to 180 degrees.
1. Angle ACD measures 63 degrees.
2. Angle CAD measures 36 degrees.
3. Angle DAB measures 13 degrees.
Using the fact that the angles in a triangle add up to 180 degrees, we can find angle CDA:
180 - 63 - 36 = x + 13
81 = x + 13
x = 81 - 13
x = 68
Now, we can find angle CBA:
180 - 63 - 36 = y
81 = y
Finally, we can find angle ADB:
180 - 13 - 68 = z
99 = z
Therefore, the values of x, y, and z are 68, 81, and 99 degrees respectively.
To find the values of x, y, and z, we can use the properties of triangles and the fact that the sum of angles in a triangle is always 180 degrees.
Given:
Angle ACD = 63 degrees
Angle CAD = 36 degrees
Angle DAB = 13 degrees
Step 1: Find Angle CDA
The sum of angles in triangle ACD is 180 degrees.
So, Angle CDA + Angle DCA + Angle ACD = 180 degrees
x + 63 + 36 = 180
x + 99 = 180
x = 180 - 99
x = 81 degrees
Step 2: Find Angle CAB
The sum of angles in triangle CAB is 180 degrees.
So, Angle CAB + Angle ABC + Angle BCA = 180 degrees
36 + y + 81 = 180
y + 117 = 180
y = 180 - 117
y = 63 degrees
Step 3: Find Angle ADB
The sum of angles in triangle ADB is 180 degrees.
So, Angle ADB + Angle DAB + Angle ABD = 180 degrees
z + 13 + (180 - x) = 180
z + 13 + (180 - 81) = 180
z + 13 + 99 = 180
z + 112 = 180
z = 180 - 112
z = 68 degrees
Therefore, the values of x, y, and z are:
x = 81 degrees
y = 63 degrees
z = 68 degrees