Math Problem Statement

Use the figure below to solve for x in the triangle with angles 17°, (3x + 7)°, and (12x - 15)°.

Solution

In the given image, we have a triangle labeled with expressions for its angles or sides. Let’s break down the problem based on what is visible.

From what I can observe:

  1. The angles or sides of the triangle are marked as:

    • A=17\angle A = 17^\circ
    • B=(3x+7)\angle B = (3x + 7)^\circ
    • C=(12x15)\angle C = (12x - 15)^\circ
  2. Since these are angles in a triangle, we can use the Triangle Sum Theorem, which states that the sum of the angles in a triangle is 180180^\circ.

Steps to Solve for xx:

  1. Set up the equation based on the angle sum: 17+(3x+7)+(12x15)=18017 + (3x + 7) + (12x - 15) = 180

  2. Simplify and combine like terms: 3x+12x+17+715=1803x + 12x + 17 + 7 - 15 = 180 15x+9=18015x + 9 = 180

  3. Isolate xx: 15x=17115x = 171 x=17115x = \frac{171}{15} x=11.4x = 11.4

So, x=11.4x = 11.4.

Would you like a detailed explanation of each step, or do you have any further questions?

Here are some related questions to explore further:

  1. How do we use the Triangle Inequality Theorem in problems involving side lengths?
  2. What other theorems are useful when working with angles in polygons?
  3. How would this problem change if it involved exterior angles?
  4. What is the Triangle Sum Theorem and how is it applied in different polygons?
  5. How would you check the consistency of your solution in a triangle problem?

Tip: Always double-check your angle sums in geometry problems involving triangles to ensure they add up to 180180^\circ.

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Math Problem Analysis

Mathematical Concepts

Algebra
Triangle Angle Sum Theorem

Formulas

Triangle Angle Sum: ∠A + ∠B + ∠C = 180°

Theorems

Triangle Angle Sum Theorem

Suitable Grade Level

Grades 8-10