Question

In the accompanying diagram, angle AEC =4x-40 and angle BED =x+50. Find measure of angle AEC.

Answer 1

Given:

`\begin{gathered} m\angle AEC\text{ = 4x -40} \\ m\angle BED\text{ = x + 50} \end{gathered}`

Angles AEC and BED are vertically opposite angles. Hence, we can write:

`\begin{gathered} 4x\text{ - 40 = x + 50} \\ \text{Collect like terms} \\ 4x\text{ -x = 50 + 40} \\ 3x\text{ = 90} \\ \text{Divide both sides by 3} \\ (3x)/(3)\text{ = }(90)/(3) \\ x\text{ = 30} \end{gathered}`

The number of degrees in angle AEC:

`\begin{gathered} m\text{ }\angle AEC=(4x-40)^0 \\ =\text{ (4 }*30-40)^0 \\ =(120-40)^0 \\ =80^0 \end{gathered}`

Answer:

The measure of angle AEC = 80 degrees