Geometry

Question Analysis

This question involves the concept of vertical angles in geometry.

 

Key Concept Explanation:

Vertical angles are formed when two lines intersect. They are non - adjacent angles opposite each other, and vertical angles are congruent.

 

Step-by-Step Solution

1. Observe the figure: The angle measuring 158° and the angle measuring (6x - 10)° are vertical angles.

2. Since vertical angles are congruent, we can set up the equation:

6x - 10 = 158.

3. Solve the equation for x:

Add 10 to both sides of the equation: 6x - 10+10 = 158 + 10, which simplifies to 6x = 168.

Divide both sides by 6: 6x÷6 = 168÷6, so x = 28.

 

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