Question

In ABCD, BD is extended through point D to point E, m_BCD = (2x - 1)º,mZCDE = (7x – 19)", and m_DBC = (x + 10). Find m2CDE.

Answer 1

We know that the exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles. In this case this means that:

`7x-19=2x-1+x+10`

Solving for x we have:

`\begin{gathered} 7x-19=2x-1+x+10 \\ 7x-19=3x+9 \\ 7x-3x=19+9 \\ 4x=28 \\ x=(28)/(4) \\ x=7 \end{gathered}`

Once we know the value of x we pluf it in the expression for the angle we want:

`7\cdot7-10=49-10=30`

Therefore, the angle CDE is 30°.