Question

find the value of x.

Explanation:

Step1: Find the adjacent interior angle

The adjacent interior angle to \(135^{\circ}\) is \(180 - 135=45^{\circ}\) (linear - pair of angles: sum is \(180^{\circ}\)).

Step2: Use the property of isosceles triangle

Since the two sides of the triangle are equal (marked with the same symbol), the triangle is isosceles. In an isosceles triangle, the base - angles are equal. Let the base - angles be \(x\) and \(45^{\circ}\). By the angle - sum property of a triangle (\(x + x+45 = 180\)).
Simplify the equation: \(2x=180 - 45\).
\(2x = 135\).
Solve for \(x\): \(x=\frac{135}{2}=67.5\).

Answer:

\(67.5\)