In the figure below, A, D, B, and G are collinear. If

ZCAD measures 76°, ZBCD measures 47°, and ZCBG
measures 140°, what is the degree measure of ZACD?
C
F. 12°
G. 14°
H. 17°
J. 36°
K. 43°

1 answer

To find the degree measure of angle ZACD, we need to first find the degree measure of angle CAD. Since angles CAD and DBC are on a straight line, they add up to 180°.

So, angle CAD = 180° - 76° = 104°

Now, angles CAD and BCG form a straight line, so they also add up to 180°.

Therefore, angle BCG = 180° - 140° = 40°

Since angles BCG and BCD are adjacent angles, they add up to 180°.

Therefore, angle BCD = 180° - 40° = 140°

Now, angles ZCAD and ZBCD are vertically opposite angles, so they are equal.

Therefore, angle ZACD = angle ZCAD + angle CAD = 76° + 104° = 180° - 140° = 40°

Therefore, the degree measure of angle ZACD is 40°.

So, the correct answer is J. 36°.