Find Angle Alpha: Solving 2x+30 and x+30 in Intersecting Lines

To find the size of angle $\alpha$, we proceed as follows:

• Step 1: Establish the relationship for the angles as supplementary: $\alpha + (2x + 30) = 180^\circ$.
• Step 2: Substitute $\alpha = x + 30$ into the equation:

Substituting, we get:

$(x + 30) + (2x + 30) = 180$

Combine like terms:

$3x + 60 = 180$

Step 3: Solve for $x$:
Subtract 60 from both sides:

$3x = 120$

Divide both sides by 3:

$x = 40$

• Step 4: Substitute $x = 40$ back into $\alpha = x + 30$ to find $\alpha$:

$\alpha = 40 + 30 = 70$

Thus, the size of the angle $\alpha$ is 70.