Question

1. (8x - 23)° 34° x = ___

Explanation:

Step1: Recall isosceles - triangle property

In an isosceles triangle, the base - angles are equal. The angle \((8x - 23)^{\circ}\) and the non - marked angle are equal. The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(34+(8x - 23)+(8x - 23)=180\).

Step2: Simplify the left - hand side of the equation

First, combine like terms: \(34+16x-46 = 180\), which simplifies to \(16x - 12=180\).

Step3: Solve for \(x\)

Add 12 to both sides of the equation: \(16x=180 + 12\), so \(16x=192\). Then divide both sides by 16: \(x=\frac{192}{16}=12\).

Answer:

\(12\)