Question

The measure of ∠ABD is (0.19x+65)° and the measure of ∠CBD is (0.06x+50)°. Find the value of x.

Answer 1

Supplementary angles are those angles that add up to 180 degrees.

In this case, analyzing the figure shown in the exercise, you can identify that the angle ABD and the angle CBD are Supplementary angles.

Based on the explained above, you can set up the following equation:

`m\angle ABD+m\angle CBD=180`

Knowing that:

`\begin{gathered} m\angle ABD=0.19x+65 \\ m\angle CBD=0.06x+50 \end{gathered}`

You can substitute them into the first equation:

`(0.19x+65)+(0.06x+50)=180`

Finally, solve for "x":

`\begin{gathered} 0.19x+65+0.06x+50=180 \\ 0.25x+115=180 \\ 0.25x=180-115 \\ \\ x=(65)/(0.25) \\ \\ x=260 \end{gathered}`

The answer is:

`x=260`