Math Problem Statement

Find the value of x given the angles of a quadrilateral: (9x - 8)°, (x + 10)°, (x + 2)°, and one unknown angle.

Solution

The image shows a quadrilateral with four angles labeled in terms of xx:

  • Top-left angle: (9x8)(9x - 8)^\circ
  • Top-right angle: (x+10)(x + 10)^\circ
  • Bottom-right angle: (x+2)(x + 2)^\circ
  • Bottom-left angle: (unlabeled, but implied to complete the set of four angles in the quadrilateral).

Since the sum of the interior angles of any quadrilateral is 360360^\circ, we can set up the equation for the sum of the four angles and solve for xx.

Step 1: Set up the equation

Let’s add all the given angles:

(9x8)+(x+10)+(x+2)+θ=360(9x - 8) + (x + 10) + (x + 2) + \theta = 360^\circ

Where θ\theta is the missing angle (which we can find by solving for xx).

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Math Problem Analysis

Mathematical Concepts

Geometry
Quadrilateral
Angles

Formulas

Sum of interior angles of a quadrilateral = 360°

Theorems

Angle sum property of quadrilaterals

Suitable Grade Level

Grades 8-10