Math Problem Statement

Solve for x in a triangle with angles 70°, 63°, and x + 56°.

Solution

This is a triangle problem where you are asked to solve for xx.

Solution Steps:

In a triangle, the sum of the interior angles is always 180180^\circ. The angles given are:

  • 7070^\circ,
  • 6363^\circ,
  • The remaining angle is represented as x+56x + 56^\circ.

To solve for xx, set up the equation using the fact that the sum of the angles in a triangle is 180180^\circ:

70+63+(x+56)=18070^\circ + 63^\circ + (x + 56^\circ) = 180^\circ

Now, combine the constants on the left-hand side:

133+x+56=180133^\circ + x + 56^\circ = 180^\circ

Simplify further:

189+x=180189^\circ + x = 180^\circ

Now, solve for xx:

x=180189x = 180^\circ - 189^\circ x=9x = -9^\circ

Thus, x=9x = -9^\circ.

Let me know if you'd like further clarification or additional details!

Related Questions:

  1. What are the interior angles of an equilateral triangle?
  2. How do you solve for angles in an isosceles triangle?
  3. What is the exterior angle theorem in triangles?
  4. How do you prove that the sum of the angles in any triangle is 180180^\circ?
  5. How do you calculate the angles of a triangle given two sides and one angle?

Tip:

When solving for angles, always double-check that the sum of the angles adds up to 180180^\circ to avoid errors!

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangles

Formulas

Sum of angles in a triangle: A + B + C = 180°

Theorems

Triangle Angle Sum Theorem

Suitable Grade Level

Grades 7-10