Answer:
In triangle ABC, we are given that ZC is a right angle (90 degrees), and CD is the altitude to AB. We are also given the measure of angle ZA (mZA) as 65 degrees.
To find the angles in CBD and CAD, we can use trigonometric relationships in right triangles:
1. Angle CBD (mDBC):
Since CD is the altitude to AB, angle CBD is the complement of angle ZA.
mDBC = 90° - mZA = 90° - 65° = 25°
2. Angle CAD (mCAD):
Angle CAD is also complementary to angle ZA because triangle CAD is a right triangle.
mCAD = 90° - mZA = 90° - 65° = 25°
3. Angle DCB (mDCB):
Angle DCB is the remaining angle in triangle DBC.
mDCB = 180° - (mDBC + mCDB) = 180° - (25° + 90°) = 180° - 115° = 65°
4. Angle CDB (mCDB):
Angle CDB is equal to angle ZA (mZA).
mCDB = mZA = 65°
5. Angle ACD (mACD):
Angle ACD is complementary to angle CAD.
mACD = 90° - mCAD = 90° - 25° = 65°
6. Angle ZADC (mZADC):
This angle is supplementary to angle ZA.
mZADC = 180° - mZA = 180° - 65° = 115°
So, here are the angle measures:
- mDBC = 25°
- mDCB = 65°
- mCDB = 65°
- mACD = 65°
- mZADC = 115°