Question

question 12
solve for x.
(11x - 65)°
78°

Explanation:

Step1: Recall isosceles - triangle property

In an isosceles triangle, the base - angles are equal. The given triangle has two equal - length sides, so the angle opposite the other non - marked side is also \(78^{\circ}\).

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(78^{\circ}+78^{\circ}+(11x - 65)^{\circ}=180^{\circ}\).
First, simplify the left - hand side: \(156+(11x - 65)=180\).
Then, \(11x+91 = 180\).
Next, subtract 91 from both sides: \(11x=180 - 91\).
So, \(11x = 89\).
Finally, divide both sides by 11: \(x=\frac{89}{11}\approx8.09\).

Answer:

\(x = \frac{89}{11}\)