Question

6 copy the triangle with the given angle measures. find the incenter. then construct the inscribed circle.
scribble

Explanation:

Step1: Copy the triangle

Use a ruler and protractor to replicate triangle \(ABC\) with \(\angle A = 45^{\circ}\), \(\angle B=80^{\circ}\), and \(\angle C = 55^{\circ}\).

Step2: Find the in - center

Construct the angle bisectors of \(\angle A\), \(\angle B\), and \(\angle C\). The point of intersection of these angle bisectors is the in - center \(I\) of the triangle.

Step3: Construct the inscribed circle

From the in - center \(I\), draw a perpendicular to one of the sides (say \(AC\)). Let the foot of the perpendicular be \(D\). With \(I\) as the center and \(ID\) as the radius, draw a circle. This is the inscribed circle (incircle) of the triangle.

Answer:

Follow the above three - step construction process to copy the triangle, find the in - center, and construct the inscribed circle.