Answer:
x = 35°, Angle 1 = 145°, Angle 2 = 35°
Step-by-step explanation:
In a trapezoid, the angles on the same leg are supplementary, meaning they add up to 180°. That means Angle 2 plus Angle 1 equals 180°. Therefore:
[tex](4x+5)+x=180^{\circ}\\5x+5=180^{\circ}\\5x=175^{\circ}\\x=35^{\circ}[/tex]
Therefore, x = 35°, Angle 2 = 35°, and Angle 1 =
[tex]4x-5^{\circ}\\4(35^{\circ})+5^{\circ}\\140^{\circ}+5^{\circ}=145^{\circ}[/tex]
To ensure our answers make sense, we verify they equal 180°:
[tex]145^{\circ}+35^{\circ}=180^{\circ}[/tex]
