Question

question
a side of the triangle below has been extended to form an exte
find the value of $x$.
answer attempt 1 out of 2
$x = $

Explanation:

Step1: Find adjacent interior angle

The 165° angle and its adjacent interior angle are supplementary (form a straight line).
$180^\circ - 165^\circ = 15^\circ$

Step2: Use triangle angle sum property

The sum of angles in a triangle is $180^\circ$. Let the unknown interior angle be $y$, so:
$15^\circ + 119^\circ + y = 180^\circ$
$y = 180^\circ - 15^\circ - 119^\circ = 46^\circ$

Step3: Relate y to x

$x$ and $y$ are supplementary (form a straight line):
$x = 180^\circ - 46^\circ = 134^\circ$
Alternative Step: Use exterior angle theorem
The exterior angle (165°) equals the sum of the two non-adjacent interior angles ($x$ is not the right angle here, correct: the exterior angle 165° = 119° + (180° - x), solve for x:
$165 = 119 + 180 - x$
$x = 119 + 180 - 165 = 134$

Answer:

$134$