Question

solve for x.

question 12
6.25 pts
use the perpendicular bisector theorem to find hg.

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
In \(\triangle UVW\), \(\angle VWZ=(21x + 1)+(11x + 1)\)
Since \(\angle VWZ = 130^{\circ}\), we have the equation \(21x+1+11x + 1=130\)

Step2: Simplify the equation

Combine like terms: \(32x+2 = 130\)
Subtract 2 from both sides: \(32x=130 - 2=128\)

Step3: Solve for \(x\)

Divide both sides by 32: \(x=\frac{128}{32}=4\)

for Question 12:

Step1: Apply the Perpendicular Bisector Theorem

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Since \(GJ\) is the perpendicular bisector of \(FH\), then \(GF = GH\)
Given \(GF = 14\), by the Perpendicular Bisector Theorem, \(GH=14\)

Answer:

\(4\)