Question

Saul creates a piece of art. He begins with the figure shown, where stack Z Y with left right arrow on top space parallel to space stack A B with left right arrow on top and m angle W Z X equal 82 degree.

MAGEO091210309_1.gif

Saul draws a line located below and parallel to stack A B with left right arrow on top that intersects stack Z A with left right arrow on top at C and stack Z B with left right arrow on top at D. The measure of angle B D C equal 56 degree. What is the measure of angle A C D ?

Answer 1

angle ACD= 138 degrees

Explanation:

As angle W Z X is opposite to the angle CZD. Angle CZD is also 82 degree.

If we consider the triangle CZD the angle D is equal to 180 - 56 = 124 degrees.( angles on a straight line= 180)

The sum of the angles of a triangle is equal to 180 degrees

<C+<D +<Z= 180

<C= 180- 82-56

<C= 42 degrees

Since Angle DCZ= 42 degrees

angle ACD= 180-42 ( angles on a straight line)

angle ACD= 138 degrees

Check

angle ACD+Angle BDC+Angle ABD + angleCAB

138+ 56+124+42 = 360 degrees