Question

16 determine the value of x in the figure shown. a 29° b 14° c 24° d 53°

Explanation:

Step1: Find the non - x angle in the small triangle

The angle adjacent to the $127^{\circ}$ angle in the small triangle forms a linear - pair. So, its measure is $180 - 127=53^{\circ}$ since the sum of angles in a linear - pair is $180^{\circ}$.

Step2: Use the angle - sum property of a triangle

In the small triangle, we know one angle is $29^{\circ}$ and another is $53^{\circ}$. According to the angle - sum property of a triangle (the sum of interior angles of a triangle is $180^{\circ}$), we can find $x$. Let the angles of the triangle be $29^{\circ}$, $53^{\circ}$, and $x$. Then $x = 180-(29 + 53)$.
$x=180 - 82=98 - 82 = 24^{\circ}$

Answer:

C. $24^{\circ}$