Section: Mathematics Usage

14)
In the figure AB = BC, CD = BD, and angle CAD = 70. What is the measure of angle ADC?

1. 80
2. 70
3. 60
4. 50
5. This cannot be determined from the information provided.

Because we know that AB = BC, then we know ABC is an isosceles triangle. Therefore, Angle CAD and angle ACB must be equal, and we know Angle CAD = 70 degres. So, Angle ACB is also 70 degrees. And because a triangle has 180 degrees total, we know Angle B equals 40 degrees.

Now, because BD = CD, we know this too is an isosceles triangle. Therefore Angle BCD also must equal 40 degrees making Angle BDC equal to 100 degrees. Now we know ADB is a straight line, so this is 180 degrees total, and when we subtract off the 100 degrees for Angle BDC, we have 80 degrees for Angle ADC