Question

In the given figure, find the mesure of angle BCD

Answer 1

Since the sum of angles in a triangle is 180°, it follows that;

`\begin{gathered} 4x+3x+2x=180 \\ 9x=180 \\ \text{ Divide both sides of the equation by }9 \\ (9x)/(9)=(180)/(9) \\ x=20 \end{gathered}`

Since line segment AB is parallel to the line segment CD, it follows from the Corresponding angles theorem that:

`\begin{gathered} \angle{B}=\angle{BCD} \\ \text{ Therefore:} \\ \angle{BCD}=4x \\ \text{ Substitute }x=20\text{ into the equation} \\ \angle{BCD}=4*20=80 \end{gathered}`

Therefore, The req