Let the size of angle $A$ be denoted as $x$ degrees.

Given:

• The size of angle $B$ is 44 times the size of angle $A$, so angle $B = 44x$.
• The size of angle $C$ is 99 degrees less than 55 times the size of angle $A$, so angle $C = 55x - 99$.

We know that the sum of the angles in a triangle is always 180 degrees:

$A + B + C = 180^\circ$ Substituting the expressions for $A$, $B$, and $C$: $x + 44x + (55x - 99) = 180$ Simplifying the equation: $x + 44x + 55x - 99 = 180$ $100x - 99 = 180$ Adding 99 to both sides: $100x = 279$ Dividing by 100: $x = 2.79$

Now, we can calculate the sizes of the angles:

• $A = x = 2.79^\circ$
• $B = 44x = 44 \times 2.79 = 122.76^\circ$
• $C = 55x - 99 = 55 \times 2.79 - 99 = 153.45 - 99 = 54.45^\circ$

Therefore, the angles are:

• $A = 2.79^\circ$
• $B = 122.76^\circ$
• $C = 54.45^\circ$

Would you like further details on any step?

Here are 5 related questions to deepen understanding:

1. How do you verify if the sum of the angles in a triangle is correct?
2. What happens if one of the angle relations is changed, e.g., $B$ is 45 times $A$?
3. Can a triangle have two angles larger than 90 degrees? Why or why not?
4. How can you express the relationship between angles of a triangle using algebraic equations?
5. What are the properties of a triangle with one angle being much smaller than the others?

Tip: In any triangle, the sum of the angles is always 180 degrees, which is a key fact to remember in solving angle problems.