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

Question

$∢B$ is 2 times bigger than $∢A$ and $∢C$ is 3 times bigger than $∢B$ .

Calculate $∢A$ .

00:00 Calculate angle A

00:05 The sum of angles in a triangle equals 180

00:11 Let's substitute appropriate values according to the given data and solve for angle B

00:21 Let's group terms

00:31 Let's isolate angle B

00:41 This is angle B

00:47 Let's substitute this value in the expression for angle A to find angle A

00:55 And this is the solution to the problem

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 $∢A = 20^\circ$ .

20°