Question

If angle 3 is a right angle, find angle 2

Answer 1

∠2=37°

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°