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Question

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.

Answer 1

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.