Question

using the angle sum and exterior angle of triangles and the angle criterion for similarity of triangles
1 use the diagram to fill in the blanks.
d = __, because 180 - ( + ) = __.
diagram of a triangle with angles 63° and 47°, and an exterior angle d°

Explanation:

Step1: Identify interior angles

The triangle has interior angles $63^\circ$, $47^\circ$, and the angle adjacent to $q^\circ$.

Step2: Apply triangle angle sum

First, find the adjacent interior angle:
$180 - (63 + 47) = 180 - 110 = 70$

Step3: Use linear pair property

$q$ and the $70^\circ$ angle form a linear pair:
$180 - 70 = 110$
Alternatively, use the exterior angle theorem: $q = 63 + 47 = 110$

Answer:

$q = 110^\circ$, because $180 - (63 + 47) = 70$ and $180 - 70 = 110$.
Or using the exterior angle property directly: $q = 63 + 47 = 110^\circ$