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?
F. 12°
G. 14°
H. 17°
J. 36°
K. 43°

1 answer

To find the degree measure of angle ZACD, we need to add up the measures of all the angles in the triangle ACD and then subtract this sum from 180° (since the angles in a triangle add up to 180°).

ZCAD = 76°
ZBCD = 47°
ZCBG = 140°

First, we find the measure of angle ACD:
ACD = ZCAD + ZBCD
ACD = 76° + 47°
ACD = 123°

Next, we find the measure of angle ZACD:
ZACD = 180° - (ACD + ZBCD)
ZACD = 180° - (123° + 47°)
ZACD = 180° - 170°
ZACD = 10°

Therefore, the degree measure of angle ZACD is 10°. This answer is not among the options provided in the choices, so there may have been a mistake in the calculations.