Question

5 137° 102° ?

Explanation:

Step1: Find the adjacent - interior angle

The adjacent - interior angle to the 137° exterior angle is found by subtracting the exterior angle from 180°. So, $180 - 137=43^{\circ}$.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Let the unknown angle be $x$. We know two interior angles of the triangle are 43° and 102°. Then $x=180-(43 + 102)$.
First, calculate the sum of the two known interior angles: $43+102 = 145^{\circ}$.
Then, find the unknown angle: $180-145 = 35^{\circ}$.

Step3: Find the exterior angle

The exterior angle adjacent to the unknown interior angle of the triangle is found by subtracting the interior angle from 180°. So, $180 - 35=145^{\circ}$.

Answer:

$145^{\circ}$