Question

1 determine the value of x in the diagram below. the diagram is not drawn to scale.

Explanation:

Step1: Find third - angle of right - hand triangle

The sum of angles in a triangle is 180°. Let the third angle of the right - hand triangle be $y$. So, $y=180^{\circ}-(83^{\circ}+35^{\circ})$.
$y = 180^{\circ}-118^{\circ}=62^{\circ}$

Step2: Use vertical - angle property

The angle $x$ and the angle $y$ are vertical angles. Vertical angles are equal. So $x = y$.
$x=62^{\circ}$

Answer:

$62^{\circ}$