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Triangle with algebraic expressions representing its side lengths.

Triangle ABC with side lengths labeled as 3x + 28, 5x + 52, and 2x - 10.

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Show Answer Key & Explanations Step-by-step solution for: Triangle angle sum Worksheets

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I need to solve for x in this triangle. Let me work through this step by step.

In any triangle, the sum of all three angles equals 180 degrees.

The three angles are:
- Angle A: 3x + 28
- Angle B: 5x + 52
- Angle C: 2x - 10

Let me set up the equation:
(3x + 28) + (5x + 52) + (2x - 10) = 180

Now let me combine like terms:
3x + 5x + 2x = 10x
28 + 52 - 10 = 70

So: 10x + 70 = 180

Subtract 70 from both sides:
10x = 110

Divide by 10:
x = 11

Let me verify this answer by checking if the angles add up to 180:
- Angle A: 3(11) + 28 = 33 + 28 = 61°
- Angle B: 5(11) + 52 = 55 + 52 = 107°
- Angle C: 2(11) - 10 = 22 - 10 = 12°

Check: 61 + 107 + 12 = 180 ✓

The answer checks out!

Final Answer:
x = 11

Parent Tip: Review the logic above to help your child master the concept of triangle angle sum worksheet.

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