Question

11)
12)
13)
14)

1. ( mangle2 = x + 94 )
2. ( mangle2 = 4x - 2 )
3. ( mangle2 = 12x + 4 )
4. ( mangle2 = 13x + 3 )

Explanation:

Since the problem set contains multiple geometry - related questions (like angle calculations, triangle properties, etc.), we'll solve one of them, say question 14.

Step 1: Identify the property

In an isosceles triangle (or a triangle with congruent sides) with a perpendicular bisector, the segments created on the base are equal. Here, the triangle is isosceles (marked with congruent sides), and the line from the vertex is a bisector, so \(12 = 2x - 12\).

Step 2: Solve for x

Add 12 to both sides of the equation: \(12+ 12=2x-12 + 12\), which simplifies to \(24 = 2x\).
Divide both sides by 2: \(\frac{24}{2}=\frac{2x}{2}\), so \(x = 12\).

Answer:

\(x = 12\)