Question

find the value of $x$.
answer attempt 1 out of 2
$x = $

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
Let the non - adjacent interior angles be \(116^{\circ}\) and the other non - adjacent interior angle (let's call it \(y\)). The exterior angle is \(134^{\circ}\). But we can also use the formula \(x + 134=180\) (linear pair) or the exterior - angle related formula in another way.

Another approach: The sum of the interior angles of a triangle is \(180^{\circ}\). Let the third interior angle of the triangle (adjacent to \(134^{\circ}\)) be \(z\), so \(z = 180 - 134=46^{\circ}\). Then, using the sum of interior angles of a triangle (\(z + 116+x'=180\), where \(x'\) is the angle adjacent to \(x\) in the linear pair). But using the exterior - angle formula directly: \(x=116+(180 - 134)\)

Step2: Calculate the value of \(x\)

First, find the non - adjacent interior angle (not \(116^{\circ}\)) which is \(180 - 134 = 46^{\circ}\). Then, by the exterior - angle theorem (the exterior angle \(x\) of the triangle is equal to the sum of the two non - adjacent interior angles), \(x=116+(180 - 134)\)

$$x=116 + 46$$

$$x = 82$$

Answer:

\(82\)