Question

21
find the measure of the unknown angle
e
c
t
?
140°
45°
d

Explanation:

Step1: Find the adjacent angle of \(140^{\circ}\)

The adjacent angle of \(140^{\circ}\) is \(180^{\circ}- 140^{\circ}=40^{\circ}\)

Step2: Use the sum of interior angles of a quadrilateral

Let the unknown angle be \(x\). In the figure, considering the sum of interior angles of the quadrilateral - like shape (using the property that the sum of interior angles of a polygon with \(n = 4\) is \((4 - 2)\times180^{\circ}=360^{\circ}\), but here we can also use the angle - relation in the figure). We know that \(x+45^{\circ}+40^{\circ}+180^{\circ}=360^{\circ}\) (the straight - line at the top is \(180^{\circ}\) in a sense of the non - curved part). Another way: using the property of the sum of angles around the "corner" formed by the lines.
We can also use the property that \(x+45^{\circ}=140^{\circ}\) (by the exterior - angle property of a non - standard polygon, where \(x\) and \(45^{\circ}\) are two non - adjacent interior angles related to the exterior angle \(140^{\circ}\)).
\(x=140^{\circ}-45^{\circ}\)

Answer:

\(95^{\circ}\)