Look at triangle ABC below.
Calculate the size of angle
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Look at triangle ABC below.
Calculate the size of angle
To find the value of , follow these steps:
Step 1: Set up the equations.
We know:
-
-
Using the given condition :
Step 2: Use the triangle angle sum property.
From the triangle angle sum, we have:
Substituting the expressions for the angles:
Solving for :
Step 3: Calculate .
Since :
Therefore, the size of angle is .
60°
Indicates which angle is greater
That equation alone has infinitely many solutions! You need the triangle angle sum (A + B + C = 180°) to find the specific values. Think of it as needing two equations to solve for three unknowns.
Since ∠B = 3∠A, it's easiest to let ∠A = α (alpha). This makes ∠B = 3α, and from the constraint A + B = 2C, we get ∠C = 2α. Now you have everything in terms of one variable!
Check your algebra! In a triangle, all angles must be positive and less than 180°. If you get impossible values, you likely made an error in setting up or solving your equations.
For this problem, degrees are perfectly fine! The angle relationships work the same way. Just make sure to be consistent - don't mix degrees and radians in the same calculation.
Verify both conditions:
With angles 30°, 60°, and 90°, this is a 30-60-90 right triangle - one of the most important special triangles in geometry!
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