Calculate Angle BCD in a Quadrilateral with Given Angles 87°, 101°, and 68°

$$The data in the drawing (which we will first write mathematically, using conventional notation):

$$$$$\sphericalangle BAD=101\degree\\ \sphericalangle ABC=87\degree\\ \sphericalangle CDA=68\degree$

Find:

$\sphericalangle BCD=\text{?}$Solution:

We'll use the fact that the sum of angles in a concave quadrilateral is $360\degree$ meaning that:

1. $\sphericalangle BAD+ \sphericalangle ABC+ \sphericalangle BCD+ \sphericalangle CDA=360\degree$

$$Let's substitute the above data in 1:

2. $101 \degree+ 87 \degree+ \sphericalangle BCD+ 68 \degree=360\degree$

Now let's solve the equation we got for the requested angle, we'll do this by moving terms:

3. $\sphericalangle BCD=360\degree- 101 \degree- 87 \degree - 68 \degree$

4. $\sphericalangle BCD=104\degree$Therefore the correct answer is answer B