In triangle​ ABC, the size of angle B is 44 times the size of angle​ A, and the size of angle C is 99degrees° less than 55 times the size of angle A.
Find the size of the angles.

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.

In triangle ABC, the size of angle B is 44 times the size of angle A, and the size of angle C is 99 degrees less than 55 times the size of angle A. Find the size of the angles.

Learn how to solve for the angles in a triangle where the size of angle B is 44 times angle A, and angle C is 99 degrees less than 55 times angle A. This problem involves algebraic manipulation and basic geometry concepts, suitable for Grades 8-10.

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