Triangle Angle Calculation: Finding Angle A When B=2A and C=3B

To solve this problem, let's calculate $∢A$ with the steps outlined below:

• Step 1: Write the equations for each angle based on the given conditions: $∢B = 2A$$∢C = 3B = 3(2A) = 6A$

• Step 2: Use the sum of angles in a triangle: $∢A + ∢B + ∢C = 180^\circ$ Substitute the expressions: $A + 2A + 6A = 180$

• Step 3: Simplify the equation: $9A = 180$ Divide both sides by 9 to solve for $A$: $A = \frac{180}{9} = 20$

Therefore, the solution to the problem is $∢A = 20^\circ$.