Answer:
∠2=37°
Step-by-step explanation:
Given:
∠1=4x°
∠2=∠4 (Vertical Angle Theorem)
∠3=90°
∠4=(3x+1)°
∠4=∠2 (Vertical Angle Theorem)
∠1+∠2+∠3=180° (We use this equation in the next step)
∠1+∠3+∠4=180°
Thus, ∠2=(3x+1)°, making:
(4x)°+(3x+1)°+90°=180°
7x+91=180
7x=89
x=12
This means:
∠1=4x=4(12)=48°
∠2=3x+1=3(12)+1=37°
∠3=90°
∠4=3x+1=3(12)+1=37°
