Based on the picture, we can say that ∠FDE and ∠EDC are supplementary angles, meaning they add to 180°. Thus, we can sum up the measues of those angles to 180 and solve for [tex]x[/tex]:
[tex](x - 7) + (2x+ 1) = 180[/tex]
[tex]3x - 6 = 180[/tex]
[tex]3x =186[/tex]
- Add 6 to both sides of the equation
[tex]x = 62[/tex]
- Divide both sides of the equation by 3
We have now found that [tex]x = 62[/tex]. However, we are looking to find ∠ADC, which doesn't have any indication of measurement. However, we can see that ∠ADC and ∠FDE are vertical angles, meaning that they have the same measurement. Let's use the fact that [tex]x = 62[/tex] to find ∠FDE first.
[tex]\angle FDE = (x - 7)^{\circ} = (62 - 7)^{\circ} = 55^{\circ}[/tex]
We have found that ∠FDE is 55°. Thus, the measure of ∠ADC is 55°.
